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Journal articles on the topic 'Ubic metric and one form metric'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Zhao, Wen Jing, Yan Yan, Li Nan Shi та Bo Chao Qu. "The Projectively Flat Conditions of One Special Class (α, β)-Metrics". Advanced Materials Research 756-759 (вересень 2013): 2528–32. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.2528.

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The-metric is an important class of Finsler metrics including Randers metric as the simplest class, and many people research the Randers metrics. In this paper, we study a new class of Finsler metrics in the form ,Whereis a Riemannian metric, is a 1-form. Bengling Li had introduced the projective flat of the-Metric F. We find another method which is about flag curvature to prove the projective flat conditions of this kind of-metric.

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2

Dillen, Franki, Luc Vrancken, and Sahnur Yaprak. "Affine hypersurfaces with parallel cubic form." Nagoya Mathematical Journal 135 (September 1994): 153–64. http://dx.doi.org/10.1017/s0027763000005006.

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As is well known, there exists a canonical transversal vector field on a non-degenerate affine hypersurface M. This vector field is called the affine normal. The second fundamental form associated to this affine normal is called the affine metric. If M is locally strongly convex, then this affine metric is a Riemannian metric. And also, using the affine normal and the Gauss formula one can introduce an affine connection ∇ on M which is called the induced affine connection. Thus there are in general two different connections on M: one is the induced connection ∇ and the other is the Levi Civita

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3

Soleiman, A., and S. G. Elgendi. "Generalized second approximation Matsumoto metric." Journal of Dynamical Systems and Geometric Theories 22, no. 1&2 (2024): 65–85. https://doi.org/10.47974/jdsgt-2024-005.

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In this paper, we tackle a more general coordinate-free investigation of the second approximation Matsumoto metric. Specifically, we establish various geometric objects corresponding the second approximation Matsumoto metric L̃(x,y) = L + B + B2/L + B3/L2 in terms of the objects of L with a Finsler structure (M,L) and a one form B. Here we consider L is Finslerian and so we call L̃ the generalized second approximation Matsumoto metric. We describe the metric tensor of L̃ and its nondegeneracy. We limit the one form B to a one form associated with a concurent π-vector field in order to determin

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4

Aslam, Muhammad Suhail, Mohammad Showkat Rahim Chowdhury, Liliana Guran, Manar A. Alqudah, and Thabet Abdeljawad. "Fixed point theory in complex valued controlled metric spaces with an application." AIMS Mathematics 7, no. 7 (2022): 11879–904. http://dx.doi.org/10.3934/math.2022663.

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<abstract><p>In this article we have introduced a metric named complex valued controlled metric type space, more generalized form of controlled metric type spaces. This concept is a new extension of the concept complex valued $ b $-metric type space and this one is different from complex valued extended $ b $-metric space. Using the idea of this new metric, some fixed point theorems involving Banach, Kannan and Fisher contractions type are proved. Some examples togetheran application are described to sustain our primary results.</p></abstract>

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5

Ontaneda, Pedro. "Deforming an є-close-to-hyperbolic metric to a hyperbolic metric". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, № 3 (2018): 629–41. http://dx.doi.org/10.1017/s0308210518000021.

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We show how to deform a metric of the form g = gr + dr2 to a metric = Hr + dr2, which is a hyperbolic metric for r less than some fixed λ, and coincides with g for r large. Here by hyperbolic metric we mean a metric of constant sectional curvature equal to -1. We study the extent to which is close to hyperbolic everywhere, if we assume g is close to hyperbolic. A precise definition of the close to hyperbolic concept is given. We also deal with a one-parameter version of this problem. The results in this paper are used in the problem of smoothing Charney–Davis strict hyperbolizations.

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6

ALVES, M. "A SIMPLE LINE ELEMENT FOR THE DILATON GRAVITY." International Journal of Modern Physics D 10, no. 04 (2001): 575–78. http://dx.doi.org/10.1142/s0218271801001323.

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The metric for the two-dimensional dilaton gravity can be writen in an alternative form, similar to the two-dimensional Schwarzschild metric, and allow us the identification of some quantitiies with those equivalent in the Schwarzschild solution. This new form, however, presents a nonphysical singularity at the horizon in the same way that in the realistic four dimensional case. We show a procedure to eliminate this horizon singularity and, as an application, the resulting metric is used to obtain the associated Hawking temperature. We discuss also some differents between this metric and the S

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7

FITRIANI, FENNY, and SARI CAHYANINGTIAS. "GRAF DUAL ANTIPRISMA DAN DIMENSI METRIKNYA." E-Jurnal Matematika 10, no. 1 (2021): 6. http://dx.doi.org/10.24843/mtk.2021.v10.i01.p313.

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Dual graph is one form of graph that can only be formed from graphs whose edges do not intersect each other. One of the graphs that can be converted into dual graphs is the antiprism graph Amn . Antiprism graph Amn is a graph that is formed from the absorption of vertices in the prism graph Pmn . One of the operations performed on a graph is finding the metric dimension of the graph. These metric dimensions are looking to find a minimum cardinality value of the graph. This article discusses the metric dimensions of the dual antiprism graph A'm,n. Dimanesion of dual antiprism graph A'm,n is obt

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8

Mandal, Khageshwar. "β-Change of Riemannian Space and Special Cases of one-form β". Journal of Nepal Mathematical Society 1, № 1 (2018): 30–37. http://dx.doi.org/10.3126/jnms.v1i1.42172.

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In this paper, we consider β-change of Finsler metric L given by L = f(L; β), where f is any positively homogeneous function of degree one in L and β. The objectives of the paper are to obtain the β-change of a Riemannian space, projective change of Finsler metric and to discuss the special cases of one-form β.

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9

Dillen, Franki, та Luc Vrancken. "3-dimensional affine hypersurfaces in ℝ4 with parallel cubic form". Nagoya Mathematical Journal 124 (грудень 1991): 41–53. http://dx.doi.org/10.1017/s0027763000003767.

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In this paper, we study 3-dimensional locally strongly convex affine hypersurfaces in ℝ4. Since the publication of Blaschke’s book [B] in the early twenties, it is well-known that on a nondegenerate affine hyper-surface M there exists a canonical transversal vector field called the affine normal. The second fundamental form associated to the affine normal is called the affine metric. In the special case that M is locally strongly convex, this affine metric is a Riemannian metric. Also, using the affine normal, by the Gauss formula one can introduce an affine connection on M, called the induced

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10

MASCHLER, GIDEON. "METRIC PAIRS AND THE FUTAKI CHARACTER." International Journal of Mathematics 13, no. 01 (2002): 1–9. http://dx.doi.org/10.1142/s0129167x02001125.

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The non-vanishing of the Futaki character gives an obstruction to the existence of Kähler metrics of constant scalar curvature, having a Kähler form belonging to a fixed Kähler class [4, 6]. It is shown that, in combination with the resolution of the Calabi conjecture [18], one has an analogous obstruction on pairs of metrics having Kähler forms belonging to a fixed pair of Kähler classes. If the difference of the Futaki characters on two classes of fixed total volume does not vanish identically, there cannot exist a pair of metrics, with Kähler forms in these classes, having the same Ricci fo

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11

Shukla, H. S., та A. P. Tiwari. "Conformal Correspondence of Finsler Spaces with Special(α,β)-Metric". Journal of the Tensor Society 6, № 01 (2007): 35–41. http://dx.doi.org/10.56424/jts.v6i01.10462.

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The purpose of the present paper is to discuss the conformal transformation of a Finsler space with a special (α,β) metric given by L2 = c1α2+2c2αβ+c3β2, where c1, c2, c3 are constants,αis Riemannian metric andβis one form. We have proved that for such a Finsler metric, the Berwald spaces, the locally Minkowski spaces and the projectively flat spaces are not invariant under nonhomothetic conformal transformation.

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12

Zohrehvand, M., та H. Maleki. "On general (α,β)-metrics of Landsberg type". International Journal of Geometric Methods in Modern Physics 13, № 06 (2016): 1650085. http://dx.doi.org/10.1142/s0219887816500857.

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In this paper, we study a class of Finsler metrics, which are defined by a Riemannian metric [Formula: see text] and a one-form [Formula: see text]. They are called general [Formula: see text]-metrics. We have proven that, every Landsberg general [Formula: see text]-metric is a Berwald metric, under a certain condition. This shows that the hunting for an unicorn, one of the longest standing open problem in Finsler geometry, cannot be successful in the class of general [Formula: see text]-metrics.

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13

Heefer, Sjors, Christian Pfeifer, Jorn van Voorthuizen, and Andrea Fuster. "On the metrizability of m-Kropina spaces with closed null one-form." Journal of Mathematical Physics 64, no. 2 (2023): 022502. http://dx.doi.org/10.1063/5.0130523.

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We investigate the local metrizability of Finsler spaces with m-Kropina metric F = α1+ m β− m, where β is a closed null one-form. We show that such a space is of Berwald type if and only if the (pseudo-)Riemannian metric α and one-form β have a very specific form in certain coordinates. In particular, when the signature of α is Lorentzian, α belongs to a certain subclass of the Kundt class and β generates the corresponding null congruence, and this generalizes in a natural way to arbitrary signature. We use this result to prove that the affine connection on such an m-Kropina space is locally m

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14

Lipatova, S. Yu. "Metrics transformations preserving the types of one-dimensional minimal fillings." Filomat 33, no. 4 (2019): 1081–89. http://dx.doi.org/10.2298/fil1904081l.

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Given a class F of metric spaces and a family of transformations T of a metric, one has to describe a family of transformations T' ? T that transfer F into itself and preserve some types of minimal fillings. The article considers four cases. First, when F is the class of all finite metric spaces, T = {(M,?) ? (M, f??) | f : R>0 ? R>0}, and the elements of T' preserve all non-degenerate types of minimal fillings of four-point metric spaces and finite non-degenerate stars, and we prove that T' = {(M,?) ? (M,?? + a):a > ?a?}. Second, when F is the class of all finite metric spaces, the c

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15

Manev, Mancho. "Yamabe Solitons on Some Conformal Almost Contact B-Metric Manifolds." Mathematics 10, no. 4 (2022): 658. http://dx.doi.org/10.3390/math10040658.

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A Yamabe soliton is defined on an arbitrary almost-contact B-metric manifold, which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The cases when the given manifold is cosymplectic or Sasaki-like are studied. In this manner, manifolds are obtained that belong to one of the main classes of the studied manifolds. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the B-metric on contact distribution. In both cases, explicit

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16

SHIMIZU, T., and K. WATANABE. "A RELATIVISTIC DESCRIPTION OF GENTRY'S NEW REDSHIFT INTERPRETATION." Modern Physics Letters A 14, no. 12 (1999): 779–90. http://dx.doi.org/10.1142/s0217732399000821.

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We obtain a new expression of the Friedmann–Robertson–Walker metric, which is an analogue of a static chart of the de Sitter space–time. The reduced metric contains two functions, M(T, R) and Ψ(T, R), which are interpreted as, respectively, the mass function and the gravitational potential. We find that, near the coordinate origin, the reduced metric can be approximated in a static form and that the approximated metric function, Ψ(R) satisfies the Poisson equation. Moreover, when the model parameters of the Friedmann–Robertson–Walker metric are suitably chosen, the approximated metric coincide

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17

Yeung, Dit-Yan, Hong Chang, and Guang Dai. "A Scalable Kernel-Based Semisupervised Metric Learning Algorithm with Out-of-Sample Generalization Ability." Neural Computation 20, no. 11 (2008): 2839–61. http://dx.doi.org/10.1162/neco.2008.05-07-528.

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In recent years, metric learning in the semisupervised setting has aroused a lot of research interest. One type of semisupervised metric learning utilizes supervisory information in the form of pairwise similarity or dissimilarity constraints. However, most methods proposed so far are either limited to linear metric learning or unable to scale well with the data set size. In this letter, we propose a nonlinear metric learning method based on the kernel approach. By applying low-rank approximation to the kernel matrix, our method can handle significantly larger data sets. Moreover, our low-rank

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18

Ahmad, Daud, and Kashif Habib. "Homotheties of a Class of Spherically Symmetric Space-Time Admitting G3 as Maximal Isometry Group." Advances in Mathematical Physics 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/8195208.

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The homotheties of spherically symmetric space-time admitting G4, G6, and G10 as maximal isometry groups are already known, whereas, for the space-time admitting G3 as isometry groups, the solution in the form of differential constraints on metric coefficients requires further classification. For a class of spherically symmetric space-time admitting G3 as maximal isometry groups without imposing any restriction on the stress-energy tensor, the metrics along with their corresponding homotheties are found. In one case, the metric is found along with its homothety vector that satisfies an additio

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19

KATSUKI, MIYUKI, AKIO SUGAMOTO, and SHIN’ICHI NOJIRI. "TWO-FORM GRAVITY AND THE GENERATION OF SPACE-TIME." International Journal of Modern Physics A 11, no. 17 (1996): 3033–48. http://dx.doi.org/10.1142/s0217751x96001474.

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In the framework of the two-form gravity, which is classically equivalent to the Einstein gravity, the one-loop effective potential for the conformal factor of metric is calculated in the finite volume and in the finite temperature by choosing a temporal gauge condition. There appears a quartically divergent term which cannot be removed by the renormalization of the cosmological term and we find there is only one nontrivial minimum in the effective potential. If the cutoff scale has a physical meaning, e.g. the Planck scale coming from string theory, this minimum might explain why the space-ti

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20

Tiwari, S. K., Brijesh Kumar Maurya та C. P. Maurya. "The conformal β-change of Finsler metric and imbedding classes of their tangent spaces". International Journal of Contemporary Mathematical Sciences 19, № 1 (2024): 15–26. https://doi.org/10.12988/ijcms.2024.91875.

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We have considered the conformal β – change of Finsler metric L given by L ̅ = e^σ f(L,β ), where f is any positively homogeneous function of degree one in L and 1-form β. We have obtained that due to this change of Finsler metric, the imbedding class of their tangent Riemannian space is increased at most by two.

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21

Kushwaha, Ramdayal Singh, та Gauree Shanker. "On the ℒ-duality of a Finsler space with exponential metric αeβ/α". Acta Universitatis Sapientiae, Mathematica 10, № 1 (2018): 167–77. http://dx.doi.org/10.2478/ausm-2018-0014.

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Abstract The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αeβ/α, where α is Riemannian metric and β is a non-zero one form.

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22

Vitter, Al. "Hermitian–Einstein metrics and jumping lines forSp(n+1)-homogeneous bundles over ℙ2n+1". Mathematical Proceedings of the Cambridge Philosophical Society 114, № 3 (1993): 443–51. http://dx.doi.org/10.1017/s0305004100071735.

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Stable holomorphic vector bundles over complex projective space ℙnhave been studied from both the differential-geometric and the algebraic-geometric points of view.On the differential-geometric side, the stability ofE-→ ℙncan be characterized by the existence of a unique hermitian–Einstein metric onE, i.e. a metric whose curvature matrix has trace-free part orthogonal to the Fubini–Study Kähler form of ℙn(see [6], [7], and [13]). Very little is known about this metric in general and the only explicit examples are the metrics on the tangent bundle of ℙnand the nullcorrelation bundle (see [9] an

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23

MUKOYAMA, SHINJI, and JEAN-PHILIPPE UZAN. "EMERGENCE OF THE LORENTZIAN STRUCTURE IN CLASSICAL FIELD THEORY." International Journal of Modern Physics D 22, no. 12 (2013): 1342018. http://dx.doi.org/10.1142/s0218271813420182.

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The Lorentzian metric structure allows one to implement the relativistic notion of causality in any field theory and to define a notion of time dimension. We propose that at the microscopic level the metric is Riemannian and that the Lorentzian structure, usually thought as fundamental, is in fact an effective property, that emerges in some regions of a 4-dimensional space with a positive definite metric. We argue that a decent classical field theory for scalars, vectors and spinors in flat spacetime can be constructed, and that gravity can be included under the form of a covariant Galileon th

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24

Duggal, K. L., and R. Sharma. "Totally umbilicalCR-submanifolds of Semi-Riemannian Kaehler manifolds." International Journal of Mathematics and Mathematical Sciences 10, no. 3 (1987): 551–55. http://dx.doi.org/10.1155/s0161171287000668.

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We study totally umbilicalCR-submanifolds of a Kaehler manifold carrying a semi-Riemannian metric. It is shown that for dimension of the totally real distribution greater than one, these submanifolds are locally decomposable into a complex and a totally real submanifold of the Kaehler manifold. For dimension equal to one, we show, in particular, that they are endowed with a normal contact metric structure if and only if the second fundamental form is parallel.

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25

Manev, Mancho. "Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field." Axioms 12, no. 1 (2023): 44. http://dx.doi.org/10.3390/axioms12010044.

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A Yamabe soliton is considered on an almost-contact complex Riemannian manifold (also known as an almost-contact B-metric manifold), which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. A case in which the potential is a torse-forming vector field of constant length on the vertical distribution determined by the Reeb vector field is studied. In this way, manifolds from one of the main classes of the studied manifolds are obtained. The same class contains the conformally equivalent manifolds of cosy

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26

Khatsymovsky, V. M. "On the discrete version of the Kerr geometry." International Journal of Modern Physics A 36, no. 20 (2021): 2150130. http://dx.doi.org/10.1142/s0217751x2150130x.

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In this paper, a Kerr-type solution in the Regge calculus is considered. It is assumed that the discrete general relativity, the Regge calculus, is quantized within the path integral approach. The only consequence of this approach used here is the existence of a length scale at which edge lengths are loosely fixed, as considered in our earlier paper. In addition, we previously considered the Regge action on a simplicial manifold on which the vertices are coordinatized and the corresponding piecewise constant metric is introduced, and found that for the simplest periodic simplicial structure an

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ROBERTS, M. D. "EXACT NONNULL WAVELIKE SOLUTIONS TO GRAVITY WITH QUADRATIC LAGRANGIANS." International Journal of Modern Physics A 09, no. 02 (1994): 167–79. http://dx.doi.org/10.1142/s0217751x9400008x.

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Solutions to gravity with quadratic Lagrangians are found for the simple case where the only nonconstant metric component is the lapse N and the Riemann tensor takes the form [Formula: see text] thus these solutions depend on cross terms in the Riemann tensor and therefore complement linearized theory where it is the derivatives of the Riemann tensor that matter. The relationship of this metric to the null gravitational radiation metric of Peres is given. Gravitational energy Poynting vectors are constructed for the solutions and one of these, based on the Lanczos tensor, supports the indicati

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28

Li, Wenbin, Yang Gao, Lei Wang, Luping Zhou, Jing Huo, and Yinghuan Shi. "OPML: A one-pass closed-form solution for online metric learning." Pattern Recognition 75 (March 2018): 302–14. http://dx.doi.org/10.1016/j.patcog.2017.03.016.

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Baines, Joshua, Thomas Berry, Alex Simpson, and Matt Visser. "Painlevé–Gullstrand form of the Lense–Thirring Spacetime." Universe 7, no. 4 (2021): 105. http://dx.doi.org/10.3390/universe7040105.

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The standard Lense–Thirring metric is a century-old slow-rotation large-distance approximation to the gravitational field outside a rotating massive body, depending only on the total mass and angular momentum of the source. Although it is not an exact solution to the vacuum Einstein equations, asymptotically the Lense–Thirring metric approaches the Kerr metric at large distances. Herein we shall discuss a specific variant of the standard Lense–Thirring metric, carefully chosen for simplicity, clarity, and various forms of improved mathematical and physical behaviour, (to be more carefully defi

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30

Alibert, Y. "New metric to quantify the similarity between planetary systems: application to dimensionality reduction using T-SNE." Astronomy & Astrophysics 624 (April 2019): A45. http://dx.doi.org/10.1051/0004-6361/201834592.

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Context. Planet formation models now often consider the formation of planetary systems with more than one planet per system. This raises the question of how to represent planetary systems in a convenient way (e.g. for visualisation purpose) and how to define the similarity between two planetary systems, for example to compare models and observations. Aims. We define a new metric to infer the similarity between two planetary systems, based on the properties of planets that belong to these systems. We then compare the similarity of planetary systems with the similarity of protoplanetary discs in

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31

Tsamparlis, Michael, and Aniekan Magnus Ukpong. "Lie Symmetries of the Wave Equation on the Sphere Using Geometry." Dynamics 4, no. 2 (2024): 322–36. http://dx.doi.org/10.3390/dynamics4020019.

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A semilinear quadratic equation of the form Aij(x)uij=Bi(x,u)ui+F(x,u) defines a metric Aij; therefore, it is possible to relate the Lie point symmetries of the equation with the symmetries of this metric. The Lie symmetry conditions break into two sets: one set containing the Lie derivative of the metric wrt the Lie symmetry generator, and the other set containing the quantities Bi(x,u),F(x,u). From the first set, it follows that the generators of Lie point symmetries are elements of the conformal algebra of the metric Aij, while the second set serves as constraint equations, which select ele

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32

Matthes, Daniel, and Simon Plazotta. "A variational formulation of the BDF2 method for metric gradient flows." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 1 (2019): 145–72. http://dx.doi.org/10.1051/m2an/2018045.

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We propose a variational form of the BDF2 method as an alternative to the commonly used minimizing movement scheme for the time-discrete approximation of gradient flows in abstract metric spaces. Assuming uniform semi-convexity – but no smoothness – of the augmented energy functional, we prove well-posedness of the method and convergence of the discrete approximations to a curve of steepest descent. In a smooth Hilbertian setting, classical theory would predict a convergence order of two in time, we prove convergence order of one-half in the general metric setting and under our weak hypotheses

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Chaudhary, Himanshu, Lehel Csillag, and Tiberiu Harko. "Semi-Symmetric Metric Gravity: A Brief Overview." Universe 10, no. 11 (2024): 419. http://dx.doi.org/10.3390/universe10110419.

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We present a review of the Semi-Symmetric Metric Gravity (SSMG) theory, representing a geometric extension of standard general relativity, based on a connection introduced by Friedmann and Schouten in 1924. The semi-symmetric connection is a connection that generalizes the Levi-Civita one by allowing for the presence of a simple form of the torsion, described in terms of a torsion vector. The Einstein field equations are postulated to have the same form as in standard general relativity, thus relating the Einstein tensor constructed with the help of the semi-symmetric connection, with the ener

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34

Palmer, J. H., and R. B. Mann. "Post-Newtonian expansion of an algebraically extended theory of gravity." Canadian Journal of Physics 69, no. 5 (1991): 641–54. http://dx.doi.org/10.1139/p91-108.

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The post-Newtonian expansion is analyzed for an algebraically extended theory of gravity equivalent to a theory with a real, nonsymmetric metric, previously referred to as Algebraically Extended Hilbert Gravity (AHG). The hermiticity of the algebra-valued covariant and contravariant metrics is found to constrain the form of the expansion of the antisymmetric part of the real metric to one of two possibilities. Both of these display a qualitatively new technical feature: the lowest order equations are nonlinear, depriving the post-Newtonian expansion of its greatest asset. In one case, they lea

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35

Gusev, Alexander. "Nonsingular Metric Elastic Universe." Symposium - International Astronomical Union 168 (1996): 571–72. http://dx.doi.org/10.1017/s0074180900110721.

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In the RTFD(Gusev (1986)) the conception of a Sakharov - Wheeler Metric Elasticity(SWME)(Sakharov (1967), Wheeler (1970)) had been worked out. On the basis of the exact solutions of Einstein equations and qualitative analysis RTFD the global evolution have been studied and the phase portraits of the early Universe is being constructed. An analysis of phase portraits show on the possibility description of spontaneous creation of Universe from an initial Minkowskian's vacuum to an inflationary de Sitter space-time in the frame of phenomenological non-quantum theory (Guth (1991)). During the past

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DAVIS, ALFRED, and TRISTAN HÜBSCH. "A FERMIONIC HODGE STAR OPERATOR." Modern Physics Letters A 14, no. 15 (1999): 965–76. http://dx.doi.org/10.1142/s0217732399001036.

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A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in space–times of any dimension. This operator realizes a conjugation (pairing) not used explicitly in field theory, and induces a metric in the space of wave function(al)s just as in exterior calculus. If made real (hermitian), this induced metric turns out to be identical to the standard one constructed using hermitian conjugation; the utility of the induced complex bilinear form remains unclear.

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37

Santoro, Antonio. "Characterization of Crystal Lattices." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C1453. http://dx.doi.org/10.1107/s2053273314085465.

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At present time, crystal lattices are characterized by means of the 44 reduced forms tabulated in Int. Tables for Crystallography, Vol. A, 1983, pag.737. Recently, we have found that this classification can be improved by a more careful analysis of the metric properties of each reduced form. Foe example, we know that the reciprocal cell of a face-centered lattice is body-centerd, and vice-versa. In the orthorhombic system there are two oF reduced forms (#16 and #26) and three oI (#8, 19 and 42) and therefore there is no one to one relationship between direct and reciprocal reduced forms. In fa

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Chand, Deep, Yumnam Rohen, Singhc Surenda, and Nicola Fabiano. "Paired-Chatterjea type contractions: Novel fixed point results and continuity properties in metric spaces." Vojnotehnicki glasnik 73, no. 2 (2025): 423–49. https://doi.org/10.5937/vojtehg73-54620.

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Introduction/purpose: The paper deals with Paired-Chatterjea type contraction mappings as an extension of traditional Chatterjea type contractions that operates on three points rather than two, in the framework of standard metric spaces. Methods: The concept of Chatterjea type contraction mappings is employed in a metric space on three points rather than two using the idea of paired contraction mappings. Results: A series of corresponding properties has been discussed. Furthermore, it is established that Paired-Chatterjea type mappings form a distinct class from traditional Chatterjea type map

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Fernández Cristóbal, José Ma. "Weyl invariance in metric f(R) gravity." Revista Mexicana de Física 64, no. 2 (2018): 181. http://dx.doi.org/10.31349/revmexfis.64.181.

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We aim to derive the most general f(R) gravity theory, including thematter, so that it be Weyl invariant. Making use of the mathematicalequivalence of these theories with an type of scalar-tensor theory, and byimposing the Weyl invariance for the pure gravity as well as for the mattersector, we obtain the fundamental equation that restricts the form of V (phi) (and, accordingly, of f(R)) so that the resulting action to be Weylinvariant in the Jordan frame. We show that this action is not otherthan the so-called dilaton gravity action with one scalar eld,, whicheective mass is R and Phi depende

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Javaid, Muhammad, Hassan Zafar, Amer Aljaedi, and Abdulaziz Mohammad Alanazi. "Boundedness of Convex Polytopes Networks via Local Fractional Metric Dimension." Mathematical Problems in Engineering 2021 (December 15, 2021): 1–14. http://dx.doi.org/10.1155/2021/2058662.

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Metric dimension is one of the distance-based parameter which is frequently used to study the structural and chemical properties of the different networks in the various fields of computer science and chemistry such as image processing, pattern recognition, navigation, integer programming, optimal transportation models, and drugs discovery. In particular, it is used to find the locations of robots with respect to shortest distance among the destinations, minimum consumption of time, and lesser number of the utilized nodes and to characterize the chemical compounds having unique presentation in

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Karasev, M. V., and T. A. Osborn. "Magnetic quantization over Riemannian manifolds." Canadian Journal of Physics 84, no. 6-7 (2006): 551–56. http://dx.doi.org/10.1139/p06-027.

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We demonstrate that Weyl's pioneering idea (1918) to intertwine metric and magnetic fields into a single joint connection can be naturally realized, on the phase space level, by the gauge-invariant quantization of the cotangent bundle with magnetic symplectic form. Quantization, for systems over a noncompact Riemannian configuration manifold, may be achieved by the introduction of a magneto-metric analog of the Stratonovich quantizer — a family of invertible, selfadjoint operators representing quantum δ functions. Based on the quantizer, we construct a generalized Wigner transform that maps Hi

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Hehl, Friedrich W., Yakov Itin, and Yuri N. Obukhov. "On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics." International Journal of Modern Physics D 25, no. 11 (2016): 1640016. http://dx.doi.org/10.1142/s0218271816400162.

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In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton’s gravitostatics and to Maxwell’s electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric qui

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Biech, T., and A. Das. "On exact-shearing perfect-fluid solutions of the nonstatic spherically symmetric Einstein field equations." Canadian Journal of Physics 68, no. 12 (1990): 1403–9. http://dx.doi.org/10.1139/p90-201.

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In this paper we have sought solutions of the nonstatic spherically symmetric field equations that exhibit nonzero shear. The Lorentzian-warped product construction is used to present the spherically symmetric metric tensor in double-null coordinates. The field equations, kinematical quantities, and Riemann invariants are computed for a perfect-fluid stress-energy tensor. For a special observer, one of the field equations reduces to a form that admits wavelike solutions. Assuming a functional relationship between the metric coefficients, the remaining field equation becomes a second-order nonl

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Tsamparlis, Michael. "Linearization of Second-Order Non-Linear Ordinary Differential Equations: A Geometric Approach." Symmetry 15, no. 11 (2023): 2082. http://dx.doi.org/10.3390/sym15112082.

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Using the coefficients of a system semilinear cubic in the first derivative second order differential equations one defines a connection in the space of the independent and dependent variables, which is specified modulo two free parameters. In this way, to any such equation one associates an affine space which is not necessarily Riemannian, that is, a metric is not required. If such a metric exists, then under the Cartan parametrization the geodesic equations of the metric coincide with the system of the considered semilinear equations. In the present work, we consider semilinear cubic in the

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Blair, David E. "A Survey of Riemannian Contact Geometry." Complex Manifolds 6, no. 1 (2019): 31–64. http://dx.doi.org/10.1515/coma-2019-0002.

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AbstractThis survey is a presentation of the five lectures on Riemannian contact geometry that the author gave at the conference “RIEMain in Contact”, 18-22 June 2018 in Cagliari, Sardinia. The author was particularly pleased to be asked to give this presentation and appreciated the organizers’ kindness in dedicating the conference to him. Georges Reeb once made the comment that the mere existence of a contact form on a manifold should in some sense “tighten up” the manifold. The statement seemed quite pertinent for a conference that brought together both geometers and topologists working on c

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Ren, Ruonan, and Yongming Li. "Uncertainty relation based on metric-adjusted skew information with quantum memory." Laser Physics 33, no. 1 (2022): 015203. http://dx.doi.org/10.1088/1555-6611/aca4cb.

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Abstract The uncertainty principle is one of the most essential features of quantum mechanics. Recently, uncertainty relations of skew information have been widely studied. In this paper, general and conditional uncertainty relations based on metric-adjusted skew information are put forward to study the case of the uncertainty relation with the existence of a quantum memory for the bipartite quantum system. These uncertainty relations include the product form and the sum form. The results show that the lower bounds contain two parts: one is characterizing the degree of compatibility of two mea

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Wang, Xu, and Kai Liu. "A Crash Surrogate Metric considering Traffic Flow Dynamics in a Motorway Corridor." Journal of Advanced Transportation 2018 (June 27, 2018): 1–7. http://dx.doi.org/10.1155/2018/9349418.

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We proposed a new crash surrogate metric, i.e., the maximum disturbance that a car following scenario can accommodate, to represent potential crash risks with a simple closed form. The metric is developed in consideration of traffic flow dynamics. Then, we compared its performance in predicting the rear-end crash risks for motorway on-ramps with other two surrogate measures (time to collision and aggregated crash index). To this end, a one-lane on-ramp of Pacific Motorway, Australia, was selected for this case study. Due to the lack of crash data on the study site, historical crash counts were

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Pant, Abhijit, R. P. Pant, M. C. Joshi, and V. Rakocevic. "Fixed points of a family of mappings and equivalent characterizations." Filomat 37, no. 5 (2023): 1391–97. http://dx.doi.org/10.2298/fil2305391p.

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In the present paper we prove a fixed point theorem for a one parameter family of contractive self-mappings, of a complete metric space or a complete b-metric space, each member of which has a unique fixed point that is also the unique common fixed point of the family; the mappings may be continuous or discontinuous at the fixed point. We also prove that under the assumption of a weaker form of continuity the fixed point property for mappings satisfying the contractive conditions employed by us implies completeness of the underlying space. The characterization of completeness obtained by us no

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Bailey, Quentin G. "Construction of Higher-Order Metric Fluctuation Terms in Spacetime Symmetry-Breaking Effective Field Theory." Symmetry 13, no. 5 (2021): 834. http://dx.doi.org/10.3390/sym13050834.

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We examined the basic conservation laws for diffeomorphism symmetry in the context of spontaneous diffeomorphism and local Lorentz-symmetry breaking. The conservation laws were used as constraints on a generic series of terms in an expansion around a flat background. We found all such terms for a two-tensor coupling to cubic order in the metric and tensor field fluctuations. The results are presented in a form that can be used for phenomenological calculations. One key result is that if we preserve the underlying diffeomorphism symmetry in a spontaneous-symmetry breaking scenario, one cannot d

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BIMONTE, G., R. MUSTO, P. VITALE, and A. STERN. "2 + 1 EINSTEIN GRAVITY AS A DEFORMED CHERN-SIMONS THEORY." International Journal of Modern Physics A 13, no. 23 (1998): 4023–47. http://dx.doi.org/10.1142/s0217751x98001888.

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The usual description of (2+1)-dimensional Einstein gravity as a Chern–Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincaré gauge group symmetry by a q-deformed Poincaré gauge group symmetry, with the former symmetry recovered when q → 1. As a result, we obtain a one parameter family of Hamiltonian formulations for 2+1 gravity. Although formulated in terms of noncommuting dreibeins and spin-connection fields, our expression for the action and our field equations, appropriately ordered, are identical in form to

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