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Journal articles on the topic 'Two-dimensional Finsler space'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Kumari, Bindu, and Ekta Srivastava. "On P2-Like Finsler Spaces." Journal of the Tensor Society 3, no. 00 (2009): 49–58. http://dx.doi.org/10.56424/jts.v3i01.9971.

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In the present paper we have discussed a special form of (v) hvtorsion tensor Pijk given by Pijk = \lamda X_i X_j X_k , where X_i are covariant components of unit vectors, is a scalar function of x,y in a finsler space. Since of every two dimensional Finsler space may be written in the form, we shall say an n-dimensional Finsler space (n ) as P2-like Finsler space whose is of this form. The values and are obtained in the terms of main scalars and h-connection vectors with respect to orthonormal frame in three and four dimensional P2-like Finsler spaces

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2

Kumari, Bindu, and Ekta Srivastava. "On P2-Like Finsler Spaces." Journal of the Tensor Society 3, no. 01 (2009): 49–58. http://dx.doi.org/10.56424/jts.v3i00.9971.

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In the present paper we have discussed a special form of (v) hvtorsion tensor Pijk given by Pijk = \lamda X_i X_j X_k , where X_i are covariant components of unit vectors, is a scalar function of x,y in a finsler space. Since of every two dimensional Finsler space may be written in the form, we shall say an n-dimensional Finsler space (n ) as P2-like Finsler space whose is of this form. The values and are obtained in the terms of main scalars and h-connection vectors with respect to orthonormal frame in three and four dimensional P2-like Finsler spaces

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3

Dokur, Emrah, Salim Ceyhan, and Mehmet Kurban. "Finsler Geometry for Two-Parameter Weibull Distribution Function." Mathematical Problems in Engineering 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/9720946.

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To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape (k) and scale (c) parameters in two-dimensional Finsler space is realized using a different

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4

Huang, Libing, and Xiaohuan Mo. "On Finsler surfaces of constant curvature with two-dimensional isometry group." International Journal of Mathematics 26, no. 07 (2015): 1550046. http://dx.doi.org/10.1142/s0129167x15500469.

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In this paper, we study Finsler surfaces of constant (flag) curvature. We show that the space of those, with two-dimensional isometric group depends on two arbitrary constants. We also give a new technique to recover Finsler metrics from the specified two constants. Using this technique we obtain some new Finsler surfaces of constant flag curvature with two-dimensional isometry group.

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5

MUNTEANU, GHEORGHE, and NICOLETA ALDEA. "A COMPLEX FINSLER APPROACH OF GRAVITY." International Journal of Geometric Methods in Modern Physics 09, no. 07 (2012): 1250058. http://dx.doi.org/10.1142/s0219887812500582.

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In this paper our aim is mainly to obtain a two-dimensional complex Finsler model of the real gravitation space-time. We prove that, at least in the special case of the weakly gravitational field, this is possible and it leads to some interesting geometrical and physical aspects, such as the study of curvature invariants with respect to complex Berwald frame, intensively studied recently by us for a two-dimensional complex Finsler space. A generalization of the Klein–Gordon equation is proposed and we find solutions which are in concordance to the classical plane wave solution of momentum-ener

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6

Tripathi, Brijesh Kumar, and K. B. Pandey. "Equations of geodesics in two dimensional Finsler space with special (?,?)-metric." New Trends in Mathematical Science 2, no. 7 (2019): 237–43. http://dx.doi.org/10.20852/ntmsci.2019.362.

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7

Matsumoto, Makoto. "The inverse problem of variation calculus in two-dimensional Finsler space." Journal of Mathematics of Kyoto University 29, no. 3 (1989): 489–96. http://dx.doi.org/10.1215/kjm/1250520222.

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8

Zaripov, R. G. "Geometry of entropy functions in the extended parastatistics of non-extensive systems." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 5 (2021): 136–40. http://dx.doi.org/10.17223/00213411/64/5/136.

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The group of functions of parametric quantum entropy in extended parastatistics of nonextensive systems is determined. The metric function of Finsler geometry in the two-dimensional space of entropy functions is introduced.

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9

Cvetkovic, Milica, and Milan Zlatanovic. "New Cartan’s tensors and pseudotensors in a generalized Finsler space." Filomat 28, no. 1 (2014): 107–17. http://dx.doi.org/10.2298/fil1401107c.

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In this work we defined a generalized Finsler space (GFN) as 2N-dimensional differentiable manifold with a non-symmetric basic tensor gij(x,x?), which applies that gij_?|m(x,x?)=0; ?=1,2. Based on non-symmetry of basic tensor, we obtained ten Ricci type identities, comparing to two kinds of covariant derivative of a tensor in Rund?s sense. There appear two new curvature tensors and fifteen magnitudes, we called ?curvature pseudotensors?.

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10

CASTRO, CARLOS. "GRAVITY IN CURVED PHASE-SPACES, FINSLER GEOMETRY AND TWO-TIMES PHYSICS." International Journal of Modern Physics A 27, no. 12 (2012): 1250069. http://dx.doi.org/10.1142/s0217751x12500698.

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The generalized (vacuum) field equations corresponding to gravity on curved 2d-dimensional (dim) tangent bundle/phase spaces and associated with the geometry of the (co)tangent bundle TMd-1, 1(T*Md-1, 1) of a d-dim space–time Md-1, 1 are investigated following the strict distinguished d-connection formalism of Lagrange–Finsler and Hamilton–Cartan geometry. It is found that there is no mathematical equivalence with Einstein's vacuum field equations in space–times of 2d dimensions, with two times, after a d+d Kaluza–Klein-like decomposition of the 2d-dim scalar curvature R is performed and invol

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11

Popov, Nikolay, and Ivan Matveev. "Six-Dimensional Manifold with Symmetric Signature in a Unified Theory of Gravity and Electromagnetism." Symmetry 14, no. 6 (2022): 1163. http://dx.doi.org/10.3390/sym14061163.

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A six dimensional manifold of symmetric signature (3,3) is proposed as a space structure for building combined theory of gravity and electromagnetism. Special metric tensor is proposed, yielding the space which combines the properties of Riemann, Weyl and Finsler spaces. Geodesic line equations are constructed where coefficients can be divided into depending on the metric tensor (relating to the gravitational interaction) and depending on the vector field (relating to the electromagnetic interaction). If there is no gravity, the geodesics turn into the equations of charge motion in the electro

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12

Clayton, John D. "Generalized Finsler Geometry and the Anisotropic Tearing of Skin." Symmetry 15, no. 10 (2023): 1828. http://dx.doi.org/10.3390/sym15101828.

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A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with the microstructure. An internal state vector is introduced on each configuration, describing subscale physics. A generalized Finsler metric depends on the position and the state vector, where the latter dependence allows for both the direction (i.e., as in Finsler geometry) and magnitude. Eq

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13

Xu, Ming, and Wolfgang Ziller. "Reversible homogeneous Finsler metrics with positive flag curvature." Forum Mathematicum 29, no. 5 (2017): 1213–26. http://dx.doi.org/10.1515/forum-2016-0173.

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AbstractIn this work, we continue with the classification for positively curve homogeneous Finsler spaces {(G/H,F)}. With the assumption that the homogeneous space {G/H} is odd dimensional and the positively curved metric F is reversible, we only need to consider the most difficult case left, i.e. when the isotropy group H is regular in G. Applying the fixed point set technique and the homogeneous flag curvature formulas, we show that the classification of odd dimensional positively curved reversible homogeneous Finsler spaces coincides with that of L. Bérard Bergery in Riemannian geometry exc

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14

Atkin, C. J. "The Finsler geometry of groups of isometries of Hilbert Space." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 2 (1987): 196–222. http://dx.doi.org/10.1017/s1446788700028202.

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AbstractThe paper deals with six groups: the unitary, orthogonal, symplectic, Fredholm unitary, special Fredholm orthogonal, and Fredholm symplectic groups of an infinite-dimensional Hilbert space. When each is furnished with the invariant Finsler structure induced by the operator-norm on the Lie algebra, it is shown that, between any two points of the group, there exists a geodesic realising this distance (often, indeed, a unique geodesic), except in the full orthogonal group, in which there are pairs of points that cannot be joined by minimising geodesics, and also pairs that cannot even be

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15

Srivastava, P. K., and V. N. Jha. "On A Two Dimensional Finsler Space Whose Geodesics Are SemiElipses and Pair of Straight Lines." IOSR Journal of Mathematics 10, no. 2 (2014): 43–51. http://dx.doi.org/10.9790/5728-10274351.

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16

Koibuchi, Hiroshi, Chrystelle Bernard, Jean-Marc Chenal, et al. "Monte Carlo Study of Rubber Elasticity on the Basis of Finsler Geometry Modeling." Symmetry 11, no. 9 (2019): 1124. http://dx.doi.org/10.3390/sym11091124.

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Configurations of the polymer state in rubbers, such as so-called isotropic (random) and anisotropic (almost aligned) states, are symmetric/asymmetric under space rotations. In this paper, we present numerical data obtained by Monte Carlo simulations of a model for rubber formulations to compare these predictions with the reported experimental stress–strain curves. The model is defined by extending the two-dimensional surface model of Helfrich–Polyakov based on the Finsler geometry description. In the Finsler geometry model, the directional degree of freedom σ → of the polymers and the polymer

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17

Rim, Mrani Alaoui, and El-Amrani Abderrahim. "Improved filtering H-infinity finite frequency of Takagi-Sugeno fuzzy systems." International Journal of Power Electronics and Drive Systems (IJPEDS) 12, no. 4 (2021): 2523–30. https://doi.org/10.11591/ijpeds.v12.i4.pp2523-2530.

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The work treats the filter H-infinity finite frequency (FF) in Takagi-Sugeno (T-S) two dimensional (2-D) systems described by Fornasini-Marchesini local state-space (FM LSS) models. The goal of this work is to find an FF H-infinity T-S fuzzy filter model design in such a way that the error system is stable and has a reduced FF H-infinity performance over FF areas with noise is established as a prerequisite. Via the use of the generalized Kalman Yakubovich Popov (gKYP) lemma, Lyapunov functions approach, Finsler’s lemma, and parameterize slack

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18

Matsumoto, M. "Geodesics of two-dimensional Finsler spaces." Mathematical and Computer Modelling 20, no. 4-5 (1994): 1–23. http://dx.doi.org/10.1016/0895-7177(94)90153-8.

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19

Itin, Yakov. "Pseudo-Riemann’s quartics in Finsler’s geometry—two-dimensional case." Journal of Physics: Conference Series 2482, no. 1 (2023): 012007. http://dx.doi.org/10.1088/1742-6596/2482/1/012007.

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Abstract Finsler’s geometry usually describes an extension of Riemmann’s geometry into a direction-dependent geometric structure. Historically, the well-known Riemann’s quartic length element example served as the inspiration for this construction. Surprisingly, the covariant Fresnel equation—a fundamental dispersion relation in solid-state electrodynamics—emerges as the exact same quartic expression. As a result, Riemann’s quartic length expression can be regarded of as a mathematical representation of a well-known physical phenomenon. In this study, we offer numerous Riemann’s quartic exampl

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20

Aldea, Nicoleta. "About a special class of two-dimensional complex Finsler spaces." Indian Journal of Pure and Applied Mathematics 43, no. 2 (2012): 107–27. http://dx.doi.org/10.1007/s13226-012-0007-2.

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21

YANG, GUOJUN, and XINYUE CHENG. "Conformal invariances of two-dimensional Finsler spaces with isotropic main scalar." Publicationes Mathematicae Debrecen 81, no. 3-4 (2012): 327–40. http://dx.doi.org/10.5486/pmd.2012.5191.

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22

Matsumoto, Makoto. "The main scalar of two-dimensional Finsler spaces with special metric." Journal of Mathematics of Kyoto University 32, no. 4 (1992): 889–98. http://dx.doi.org/10.1215/kjm/1250519412.

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23

Mishra, Asmita, and Suraj Kumar Shukla. "Connections and Main Scalars of Two Dimensional Finsler Spaces with Quintic Metric." Journal of Computer and Mathematical Sciences 9, no. 6 (2018): 588–98. http://dx.doi.org/10.29055/jcms/792.

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24

Matsumoto, Makoto. "Two-dimensional Finsler spaces whose geodesics constitute a family of special conic sections." Journal of Mathematics of Kyoto University 35, no. 3 (1995): 357–76. http://dx.doi.org/10.1215/kjm/1250518701.

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25

Antonelli, P. L., and M. Matsumoto. "On conformal and projective flatness of two-dimensional constant-Berwald Finsler spaces in epidemiology." Open Systems & Information Dynamics 3, no. 3 (1995): 305–17. http://dx.doi.org/10.1007/bf02228994.

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26

Larotonda, Gabriel. "Metric geometry of infinite-dimensional Lie groups and their homogeneous spaces." Forum Mathematicum 31, no. 6 (2019): 1567–605. http://dx.doi.org/10.1515/forum-2019-0127.

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AbstractWe study the geometry of Lie groups G with a continuous Finsler metric, in presence of a subgroup K such that the metric is right-invariant for the action of K. We present a systematic study of the metric and geodesic structure of homogeneous spaces M obtained by the quotient {M\simeq G/K}. Of particular interest are left-invariant metrics of G which are then bi-invariant for the action of K. We then focus on the geodesic structure of groups K that admit bi-invariant metrics, proving that one-parameter groups are short paths for those metrics, and characterizing all other short paths.

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27

VACARU, SERGIU I. "PARAMETRIC NONHOLONOMIC FRAME TRANSFORMS AND EXACT SOLUTIONS IN GRAVITY." International Journal of Geometric Methods in Modern Physics 04, no. 08 (2007): 1285–334. http://dx.doi.org/10.1142/s0219887807002570.

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A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The new classes of solutions are defined by generic off-diagonal metrics depending on integration functions on one, two and three (or three and four) variables if we cons

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28

Alaoui, Rim Mrani, and Abderrahim El-Amrani. "Improved filtering H∞ finite frequency of Takagi-Sugeno fuzzy systems." International Journal of Power Electronics and Drive Systems (IJPEDS) 12, no. 4 (2021): 2523. http://dx.doi.org/10.11591/ijpeds.v12.i4.pp2523-2530.

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The work treats the filter H∞ finite frequency (FF) in Takagi-Sugeno (T-S) two dimensional (2-D) systems described by Fornasini-Marchesini local state-space (FM LSS)models. The goal of this work is to find an FF H∞ T-S fuzzy filter model design in such a way that the error system is stable and has a reduced FF H∞ performance over FF area swith noise is established as aprerequisite. Via the use of the generalized Kalman Yakubovich Popov (gKYP) lemma, Lyapunov functions approach, Finsler’s lemma, and parameterize slack matrices, new design conditions guaranteeing the FF H∞ T-S fuzzy filter metho

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29

H.S.Shukla and Mishra Arunima. "On Finsler Space with Randers Conformal Change — Main Scalar, Geodesic and Scalar Curvature." August 20, 2012. https://doi.org/10.5281/zenodo.823955.

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In the present paper we have found out the expressions for scalar curvature and main scalar of two-dimensional Finsler space obtained by Randers conformal change of F<sup>n</sup>. We have also obtained equation of geodesic for this transformed space.

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30

Jangir, Seema, Gauree Shanker, Jaspreet Kaur, and Laurian-Ioan Piscoran. "ON THE EXISTENCE AND EXAMPLES OF HOMOGENEOUS GEODESICS IN GENERALIZED m-KROPINA SPACE." Facta Universitatis, Series: Mathematics and Informatics, May 3, 2024, 289. http://dx.doi.org/10.22190/fumi230524020j.

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In this paper, we find a necessary and sufficient condition for a non-zero vector to be a geodesic vector in homogeneous generalized m-Kropina space. Further, we prove the existence of at least one homogeneous geodesic. However, it is conjectured that the outcomes and proofs in the case of Finsler geometry are not ideal, since general Finsler metrics are non-reversible. In Finsler geometry, the trajectory of unique homogeneous geodesic should be regarded as two geodesics with initial vectors X and -X. Hence, we construct an (n + 1)-dimensional and a 4-dimensional space to find homogeneous geod

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31

Chaubey, V. K., and B. K. Tripathi. "Finslerian hypersurfaces of a Finsler space with deformed Douglas infinite series metric." Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science, June 5, 2025, 101–14. https://doi.org/10.31926/but.mif.2025.5.67.2.8.

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In present paper we studied the geometrical properties of Finslerian hypersurfaces and its reducibility of Cartan C− tensor in various forms for a Finsler space Fn equipped with deformed Infinite series metric. Further we obtained the value of main scalar I for the hypersurface in a two-dimensional case.

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32

Chaubey, V. "ON KROPINA CHANGE OF TWO-DIMENSIONAL FINSLER SPACES." International Journal of Pure and Apllied Mathematics 82, no. 4 (2013). http://dx.doi.org/10.12732/ijpam.v82i4.8.

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33

Mao., Linfan. "An introduction to Smarandache multi-spaces and mathematical combinatorics." April 23, 2007. https://doi.org/10.5281/zenodo.9185.

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These Smarandache spaces are right theories for objectives by logic. However, the mathematical combinatorics is a combinatorial theory for branches in classical mathematics motivated by a combinatorial speculation. Both of them are unifying theories for sciences and contribute more and more to mathematics in the 21st century. In this paper, I introduce these two subjects and mainly concentrate on myself research works on mathematical combinatorics finished in past three years, such as those of map geometries, pseudo-manifolds of dimensional n, topological or di®erential structure

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