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Journal articles on the topic 'Tangent bundles'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 July 2024

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1

Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman and Makarim Abdullah Mohammed Ali Mohammed. "Investigate A New Tangent Bundle Space from A New Point and Two Curves using MATLAB." IJRDO -JOURNAL OF MATHEMATICS 10, no. 1 (January 25, 2024): 1–11. http://dx.doi.org/10.53555/m.v10i1.5979.

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Our goal was to create a new tangent bundle space from a new point and two curves using the MATLAB program. We used the applied mathematical approach, and we arrived at an accurate model of the tangent bundle space by building an algorithm that implements the solution and displays the results and represents them graphically with ease and with high accuracy. This is what MATLAB makes a suitable working environment for dealing with tangent bundles. Given the importance of tangent bundles in modern engineering and physical sciences, this algorithm can be developed to include the most important areas of tangent bundles instead of the complex traditional method

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2

ISIDRO, JOSÉ M. "QUANTUM STATES FROM TANGENT VECTORS." Modern Physics Letters A 19, no. 31 (October 10, 2004): 2339–52. http://dx.doi.org/10.1142/s0217732304015634.

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We argue that tangent vectors to classical phase space give rise to quantum states of the corresponding quantum mechanics. This is established for the case of complex, finite-dimensional, compact, classical phase spaces [Formula: see text], by explicitly constructing Hilbert-space vector bundles over [Formula: see text]. We find that these vector bundles split as the direct sum of two holomorphic vector bundles: the holomorphic tangent bundle [Formula: see text], plus a complex line bundle [Formula: see text]. Quantum states (except the vacuum) appear as tangent vectors to [Formula: see text]. The vacuum state appears as the fibrewise generator of [Formula: see text]. Holomorphic line bundles [Formula: see text] are classified by the elements of [Formula: see text], the Picard group of [Formula: see text]. In this way [Formula: see text] appears as the parameter space for nonequivalent vacua. Our analysis is modelled on, but not limited to, the case when [Formula: see text] is complex projective space CPn.

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3

Sultanov, A. Ya, G. A. Sultanova, and N. V. Sadovnikov. "Affine transformations of the tangent bundle with a complete lift connection over a manifold with a linear connection of special type." Differential Geometry of Manifolds of Figures, no. 52 (2021): 137–43. http://dx.doi.org/10.5922/0321-4796-2021-52-13.

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The theory of tangent bundles over a differentiable manifold M belongs to the geometry and topology of manifolds and is an intensively developing area of the theory of fiber spaces. The foundations of the theory of fibered spaces were laid in the works of S. Eresman, A. Weil, A. Morimoto, S. Sasaki, K. Yano, S. Ishihara. Among Russian scientists, tangent bundles were investigated by A. P. Shirokov, V. V. Vishnevsky, V. V. Shurygin, B. N. Shapukov and their students. In the study of automorphisms of generalized spaces, the question of infinitesimal transformations of connections in these spaces is of great importance. K. Yano, G. Vrancianu, P. A. Shirokov, I. P. Egorov, A. Z. Petrov, A. V. Aminova and others have studied movements in different spaces. The works of K. Sato and S. Tanno are devoted to the motions and automorphisms of tangent bundles. Infinitesimal affine collineations in tangent bundles with a synectic connection were considered by H. Shadyev. At present, the question of the motions of fibered spaces is considered in the works of A. Ya. Sultanov, in which infinitesimal transformations of a bundle of linear frames with a complete lift connection, the Lie algebra of holomorphic affine vector fields in arbitrary Weyl bundles are investigated. In this paper we obtain exact upper bounds for the dimensions of Lie algebras of infinitesimal affine transformations in tangent bundles with a synectic connection A. P. Shyrokov.

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Sultanov, A. Ya, and G. A. Sultanova. "On the local representation of synectic connections on Weil bundles." Differential Geometry of Manifolds of Figures, no. 53 (2022): 118–26. http://dx.doi.org/10.5922/0321-4796-2022-53-11.

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Synectic extensions of complete lifts of linear connections in tangent bundles were introduced by A. P. Shirokov in the seventies of the last century [1; 2]. He established that these connections are linear and are real realizations of linear connections on first-order tangent bundles endowed with a smooth structure over the algebra of dual numbers. He also proved the existence of a smooth structure on tangent bundles of arbitrary order on a smooth manifold M over the algebra of plural numbers. Studying holomorphic linear connections on over an algebra , A. P. Shirokov obtained real realizations of these connections, which he called Synectic extensions of a linear connection defined on M. A natural generalization of the algebra of plural numbers is the A. Weyl algebra, and a generalization of the tangent bundle is the A. Weyl bundle. It was shown in [3] that a synectic extension of linear connections defined on M a smooth manifold can also be constructed on A. Weyl bundles , where is the A. Weyl algebra. The geometry of these bundles has been studied by many authors — A. Morimoto, V. V. Shurygin and others. A detailed analysis of these works can be found in [3]. In this paper, we study synectic lifts of linear connections defined on A. Weyl bundles.

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5

Jacobowitz, Howard, and Gerardo Mendoza. "Sub-bundles of the complexified tangent bundle." Transactions of the American Mathematical Society 355, no. 10 (June 10, 2003): 4201–22. http://dx.doi.org/10.1090/s0002-9947-03-03350-6.

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6

Feizabadi, Hassan, and Naser Boroojerdian. "Extending Tangent Bundles by an Algebra Bundle." Iranian Journal of Science and Technology, Transactions A: Science 42, no. 2 (February 13, 2018): 615–21. http://dx.doi.org/10.1007/s40995-018-0515-y.

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7

Ali, Sahadat. "Prolongation of Tensor Fields and G-Structures in Tangent Bundles of Second Order." Journal of the Tensor Society 9, no. 01 (June 30, 2009): 77–81. http://dx.doi.org/10.56424/jts.v9i01.10563.

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Tangent and cotangent bundles have been defined and studied by Yano, Ishihara, Patterson and others. Duggal gives the notion of GF-structure, which plays an important role in the differentiable manifold [1]. R. Nivas and Ali have studied the existence of GF-structure and generalized contact structure on the tangent bundle and some interesting results have been obtained for such structures [2]. Prolongation of tensor fields, almost complex and almost product structures have been defined and studied by Yano, Ishihara [3] and others whereas Das [4] and Morimoto [5] have studied the prolongation of F-structure and G-structures respectively to the tangent bundles. In the present paper problems of prolongation in tangent bundle of second order and few results on GF, fa(3, −1) and generalized contact structures have been discussed.

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8

Li, Tongzhu, and Demeter Krupka. "The Geometry of Tangent Bundles: Canonical Vector Fields." Geometry 2013 (April 14, 2013): 1–10. http://dx.doi.org/10.1155/2013/364301.

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A canonical vector field on the tangent bundle is a vector field defined by an invariant coordinate construction. In this paper, a complete classification of canonical vector fields on tangent bundles, depending on vector fields defined on their bases, is obtained. It is shown that every canonical vector field is a linear combination with constant coefficients of three vector fields: the variational vector field (canonical lift), the Liouville vector field, and the vertical lift of a vector field on the base of the tangent bundle.

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9

CRASMAREANU, MIRCEA. "DIRAC STRUCTURES FROM LIE INTEGRABILITY." International Journal of Geometric Methods in Modern Physics 09, no. 04 (May 6, 2012): 1220005. http://dx.doi.org/10.1142/s0219887812200058.

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We prove that a pair (F = vector sub-bundle of TM, its annihilator) yields an almost Dirac structure which is Dirac if and only if F is Lie integrable. Then a flat Ehresmann connection on a fiber bundle ξ yields two complementary, but not orthogonally, Dirac structures on the total space M of ξ. These Dirac structures are also Lagrangian sub-bundles with respect to the natural almost symplectic structure of the big tangent bundle of M. The tangent bundle in Riemannian geometry is discussed as particular case and the 3-dimensional Heisenberg space is illustrated as example. More generally, we study the Bianchi–Cartan–Vranceanu metrics and their Hopf bundles.

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10

Abbassi, Mohamed Tahar Kadaoui, and Ibrahim Lakrini. "On the completeness of total spaces of horizontally conformal submersions." Communications in Mathematics 29, no. 3 (December 1, 2021): 493–504. http://dx.doi.org/10.2478/cm-2021-0031.

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Abstract In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class of Cheeger-Gromoll and generalized Cheeger-Gromoll metrics on vector bundle manifolds. Moreover, we study the completeness of a subclass of g-natural metrics on tangent bundles and we extend the results to the case of unit tangent sphere bundles. Our proofs are mainly based on techniques of metric topology and on the Hopf-Rinow theorem.

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11

Takahashi, Tomokuni. "Projective Plane Bundles Over an Elliptic Curve." Canadian Mathematical Bulletin 61, no. 1 (March 1, 2018): 201–10. http://dx.doi.org/10.4153/cmb-2017-025-8.

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AbstractWe calculate the dimension of cohomology groups for the holomorphic tangent bundles of each isomorphism class of the projective plane bundle over an elliptic curve. As an application, we construct the families of projective plane bundles, and prove that the families are effectively parametrized and complete.

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12

Das, Lovejoy S. "Complete lift of a structure satisfyingFK−(−)K+1F=0." International Journal of Mathematics and Mathematical Sciences 15, no. 4 (1992): 803–8. http://dx.doi.org/10.1155/s0161171292001042.

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The idea off-structure manifold on a differentiable manifold was initiated and developed by Yano [1], Ishihara and Yano [2], Goldberg [3] and among others. The horizontal and complete lifts from a differentiable manifoldMnof classC∞to its cotangent bundles have been studied by Yano and Patterson [4,5]. Yano and Ishihara [6] have studied lifts of anf-structure in the tangent and cotangent bundles. The purpose of this paper is to obtain integrability conditions of a structure satisfyingFK−(−)K+1F=0andFW−(−)W+1F≠0for1<W<K, in the tangent bundle.

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13

Ali, Md Showkat, Md Mirazul Islam, Farzana Nasrin, Md Abu Hanif Sarkar, and Tanzia Zerin Khan. "Connections on Bundles." Dhaka University Journal of Science 60, no. 2 (July 31, 2012): 191–94. http://dx.doi.org/10.3329/dujs.v60i2.11492.

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This paper is a survey of the basic theory of connection on bundles. A connection on tangent bundle TM, is called an affine connection on an m-dimensional smooth manifold M. By the general discussion of affine connection on vector bundles that necessarily exists on M which is compatible with tensors.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11492 Dhaka Univ. J. Sci. 60(2): 191-194, 2012 (July)

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14

Kadaoui Abbassi, Mohamed Tahar, and Noura Amri. "Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles." Axioms 9, no. 3 (June 30, 2020): 72. http://dx.doi.org/10.3390/axioms9030072.

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In this paper, we study natural paracontact magnetic trajectories in the unit tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza–Klein type metrics on their unit tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics).

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15

Thompson, G. "Integrable almost cotangent structures and Legendrian bundles." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 1 (January 1987): 61–78. http://dx.doi.org/10.1017/s030500410006641x.

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Recently, the present author together with M. Crampin proved a structure theorem for a certain subclass of geometric objects known as almost tangent structures (Crampin and Thompson [8]). As the name suggests, an almost tangent structure is obtained by abstracting one of the tangent bundle's most important geometrical ingredients, namely its canonical 1–1 tensor, and using it to define a certain class of G-structures. Roughly speaking, the structure theorem referred to above may be paraphrased by saying that, if an almost tangent structure is integrable as a G-structure and satisfies some natural global hypotheses, then it is essentially the tangent bundle of some differentiable manifold. (I shall have a further remark to make about the conclusion of that theorem at the end of Section 2.)

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16

Hsieh, Po-Hsun. "Symplectic Geometry of Vector Bundle Maps of Tangent Bundles." Rocky Mountain Journal of Mathematics 31, no. 3 (September 2001): 987–1001. http://dx.doi.org/10.1216/rmjm/1020171675.

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17

Abael Raman, Abdel Gadir, Safia Abd Elrabman Jameel Mohammed, and Abdelhakam Hassan Mohammed Tahir. "The Concept of Curvature in Fiber Bundles." International Journal of Scientific and Management Research 05, no. 03 (2022): 32–41. http://dx.doi.org/10.37502/ijsmr.2022.5304.

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Many basic concepts in theoretical physics can be interpreted in term of fiber bundles. A fiber bundle is a manifold that locally looks like a product manifold. The well-known examples are the tangent and the cotangent bundles. The aim of this paper is to discuss and explain the concept of curvature in fiber bundles. We followed the analytical induction mathematical method and we found that the curvature is very important concept in fiber bundles.We use Theory of fiber bundles to illustrate the structure homogenous C ∗ algebras.

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18

Sekizawa, Masami. "Lifts of generalized symmetric spaces to tangent bundles." Časopis pro pěstování matematiky 112, no. 3 (1987): 261–68. http://dx.doi.org/10.21136/cpm.1987.118322.

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19

PEYGHAN, ESMAEIL, AKBAR TAYEBI, and CHUNPING ZHONG. "HORIZONTAL LAPLACIAN ON TANGENT BUNDLE OF FINSLER MANIFOLD WITH g-NATURAL METRIC." International Journal of Geometric Methods in Modern Physics 09, no. 07 (September 7, 2012): 1250061. http://dx.doi.org/10.1142/s0219887812500612.

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Recently the third author studied horizontal Laplacians in real Finsler vector bundles and complex Finsler manifolds. In this paper, we introduce a class of g-natural metrics Ga,b on the tangent bundle of a Finsler manifold (M, F) which generalizes the associated Sasaki–Matsumoto metric and Miron metric. We obtain the Weitzenböck formula of the horizontal Laplacian associated to Ga,b, which is a second-order differential operator for general forms on tangent bundle. Using the horizontal Laplacian associated to Ga,b, we give some characterizations of certain objects which are geometric interest (e.g. scalar and vector fields which are horizontal covariant constant) on the tangent bundle. Furthermore, Killing vector fields associated to Ga,b are investigated.

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20

Musso, E., and F. Tricerri. "Riemannian metrics on tangent bundles." Annali di Matematica Pura ed Applicata 150, no. 1 (December 1988): 1–19. http://dx.doi.org/10.1007/bf01761461.

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21

Perrone, Domenico. "Tangent sphere bundles satisfying ???=0." Journal of Geometry 49, no. 1-2 (March 1994): 178–88. http://dx.doi.org/10.1007/bf01228060.

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22

Mitric, Gabriel, and Izu Vaisman. "Poisson structures on tangent bundles." Differential Geometry and its Applications 18, no. 2 (March 2003): 207–28. http://dx.doi.org/10.1016/s0926-2245(02)00148-1.

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23

Satoh, Takamichi, and Masami Sekizawa. "Curvatures of tangent hyperquadric bundles." Differential Geometry and its Applications 29 (August 2011): S255—S260. http://dx.doi.org/10.1016/j.difgeo.2011.04.050.

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24

Kobak, Piotr. "Natural liftings of vector fields to tangent bundles of bundles of $1$-forms." Mathematica Bohemica 116, no. 3 (1991): 319–26. http://dx.doi.org/10.21136/mb.1991.126171.

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25

Kadaoui Abbassi, Mohamed Tahar, and Noura Amri. "Natural Ricci Solitons on Tangent and Unit Tangent Bundles." Zurnal matematiceskoj fiziki, analiza, geometrii 17, no. 1 (January 25, 2021): 3–29. http://dx.doi.org/10.15407/mag17.01.003.

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26

Popov, Yu I. "Fields of geometric objects associated with compiled hyperplane-distribution in affine space." Differential Geometry of Manifolds of Figures, no. 51 (2020): 103–15. http://dx.doi.org/10.5922/0321-4796-2020-51-12.

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A compiled hyperplane distribution is considered in an n-dimensional projective space . We will briefly call it a -distribution. Note that the plane L(A) is the distribution characteristic obtained by displacement in the center belonging to the L-subbundle. The following results were obtained: a) The existence theorem is proved: -distribution exists with arbitrary (3n – 5) functions of n arguments. b) A focal manifold is constructed in the normal plane of the 1st kind of L-subbundle. It was obtained by shifting the center A along the curves belonging to the L-distribution. A focal manifold is also given, which is an analog of the Koenigs plane for the distribution pair (L, L). c) It is shown that a framed -distribution in the 1st kind normal field of H-distribution induces tangent and normal bundles. d) Six connection theorems induced by a framed -distribution in these bundles are proved. In each of the bundles , the framed -distribution induces an intrinsic torsion-free affine connection in the tangent bundle and a centro-affine connection in the corresponding normal bundle. e) In each of the bundles (d) in the differential neighborhood of the 2nd order, the covers of 2-forms of curvature and curvature tensors of the corresponding connections are constructed.

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27

SAXENA, MOHIT. "LIFTS ON THE SUPERSTRUCTURE F(±a^2,±b^2) OBEYING (F^2+a^2)(F^2-a^2)(F^2+b^2)(F^2-b^2) = 0." Journal of Science and Arts 24, no. 4 (December 30, 2023): 965–72. http://dx.doi.org/10.46939/j.sci.arts-23.4-a13.

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The purpose of the present paper is to analyze the concept of the horizontal and complete lifts on the superstructure F(±a^2,±b^2), which is defined as (F^2+a^2)(F^2-a^2)(F^2+b^2)(F^2-b^2) = 0, over the tangent bundles and establish its integrability conditions using the horizontal and complete lifts. Finally, some properties of the third-order tangent bundle are investigated.

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28

Biswas, Indranil, A. J. Parameswaran, and S. Subramanian. "Essentially finite vector bundles on varieties with trivial tangent bundle." Proceedings of the American Mathematical Society 139, no. 11 (November 1, 2011): 3821–29. http://dx.doi.org/10.1090/s0002-9939-2011-10804-9.

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29

Biswas, Indranil. "Principal bundles on compact complex manifolds with trivial tangent bundle." Archiv der Mathematik 96, no. 5 (May 2011): 409–16. http://dx.doi.org/10.1007/s00013-011-0268-8.

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30

Vyalova, A. V. "Curvature and torsion pseudotensors of coaffine connection in tangent bundle of hypercentred planes manifold." Differential Geometry of Manifolds of Figures, no. 51 (2020): 49–57. http://dx.doi.org/10.5922/0321-4796-2020-51-6.

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The hypercentered planes family, whose dimension coincides with dimension of generating plane, is considered in the projective space. Two principal fiber bundles arise over it. Typical fiber for one of them is the stationarity subgroup for hypercentered plane, for other — the linear group operating in each tangent space to the manifold. The latter bundle is called the principal bundle of linear coframes. The structural forms of two bundles are related by equations. It is proved that hypercentered planes family is a holonomic smooth manifold. In the principal bundle of linear coframes the coaffine connection is given. From the differential equations it follows that the coaffine connection object forms quasipseudotensor. It is proved that the curvature and torsion objects for the coaffine connection in the linear coframes bundle form pseudotensors.

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31

Balan, Vladimir, Maido Rahula, and Nicoleta Voicu. "Iterative calculus on tangent floors." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 1 (January 1, 2016): 121–52. http://dx.doi.org/10.1515/auom-2016-0007.

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AbstractTangent fibrations generate a “multi-floored tower”, while raising from one of its floors to the next one, one practically reiterates the previously performed actions. In this way, the "tower" admits a ladder-shaped structure. Raising to the first floors suffices for iteratively performing the subsequent steps. The paper mainly studies the tangent functor. We describe the structure of multiple vector bundle which naturally appears on the floors, tangent maps, sector-forms, the lift of vector fields to upper floors. Further, we show how tangent groups of Lie groups lead to gauge theory, and explain in this context the meaning of covariant differentiation. Finally, we will point out within the floors special subbundles - the osculating bundles, which play an essential role in classical theories.

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32

de León, M., Isabel Méndez, and M. Salgado. "Integrablep-almost tangent manifolds and tangent bundles ofp 1-velocities." Acta Mathematica Hungarica 58, no. 1-2 (March 1991): 45–54. http://dx.doi.org/10.1007/bf01903546.

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33

Plaszczyk, Mariusz. "The natural transformations between r-th order prolongation of tangent and cotangent bundles over Riemannian manifolds." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 69, no. 1 (November 30, 2015): 91. http://dx.doi.org/10.17951/a.2015.69.1.91.

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If (M, g) is a Riemannian manifold then there is the well-known base preserving vector bundle isomorphism TM → T*M given by v → g(v, –) between the tangent TM and the cotangent T*M bundles of M. In the present note first we generalize this isomorphism to the one J<sup>r</sup>TM → J<sup>r</sup>T*M between the r-th order prolongation J<sup>r</sup>TM of tangent TM and the r-th order prolongation J<sup>r</sup>T*M of cotangent T*M bundles of M. Further we describe all base preserving vector bundle maps D<sub>M</sub>(g) : J<sup>r</sup>TM → J<sup>r</sup>T*M depending on a Riemannian metric g in terms of natural (in g) tensor fields on M.

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34

Vulcu, Vlad-Augustin. "Dirac Structures on Banach Lie Algebroids." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 3 (September 1, 2014): 219–28. http://dx.doi.org/10.2478/auom-2014-0060.

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Abstract In the original definition due to A. Weinstein and T. Courant a Dirac structure is a subbundle of the big tangent bundle T M ⊕ T* M that is equal to its ortho-complement with respect to the so-called neutral metric on the big tangent bundle. In this paper, instead of the big tangent bundle we consider the vector bundle E ⊕ E*, where E is a Banach Lie algebroid and E* its dual. Recall that E* is not in general a Lie algebroid. We define a bilinear and symmetric form on the vector bundle E ⊕ E* and say that a subbundle of it is a Dirac structure if it is equal with its orthocomplement. Our main result is that any Dirac structure that is closed with respect to a type of Courant bracket, endowed with a natural anchor is a Lie algebroid. In the proof the differential calculus on a Lie algebroid is essentially involved. We work in the category of Banach vector bundles.

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35

BUCATARU, IOAN, and MATIAS F. DAHL. "Descending maps between slashed tangent bundles." Publicationes Mathematicae Debrecen 79, no. 1-2 (July 1, 2011): 231–50. http://dx.doi.org/10.5486/pmd.2011.500.

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36

Bucataru, Ioan, and Matias F. Dahl. "Descending maps between slashed tangent bundles." Publicationes Mathematicae Debrecen 79, no. 1-2 (July 1, 2011): 231–50. http://dx.doi.org/10.5486/pmd.2011.5008.

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37

Taek Cho, Jong, and Sun Hyang Chun. "Pseudo-Einstein unit tangent sphere bundles." Hiroshima Mathematical Journal 48, no. 3 (November 2018): 413–27. http://dx.doi.org/10.32917/hmj/1544238035.

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38

YAMAUCHI, Kazunari. "On conformal transformations in tangent bundles." Hokkaido Mathematical Journal 30, no. 2 (June 2001): 359–72. http://dx.doi.org/10.14492/hokmj/1350911958.

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39

Vîlcu, G. E. "Para-hyperhermitian structures on tangent bundles." Proceedings of the Estonian Academy of Sciences 60, no. 3 (2011): 165. http://dx.doi.org/10.3176/proc.2011.3.04.

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40

Gudmundsson, Sigmundur, and Elias Kappos. "On the geometry of tangent bundles." Expositiones Mathematicae 20, no. 1 (2002): 1–41. http://dx.doi.org/10.1016/s0723-0869(02)80027-5.

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41

Inoguchi, Jun-ichi, and Marian Ioan Munteanu. "Magnetic curves on tangent sphere bundles." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113, no. 3 (November 20, 2018): 2087–112. http://dx.doi.org/10.1007/s13398-018-0600-2.

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42

Ga̧sior, A., and A. Szczepański. "Tangent bundles of Hantzsche–Wendt manifolds." Journal of Geometry and Physics 70 (August 2013): 123–29. http://dx.doi.org/10.1016/j.geomphys.2013.03.013.

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43

Calvaruso, G., and D. Perrone. "$H$-Contact Unit Tangent Sphere Bundles." Rocky Mountain Journal of Mathematics 37, no. 5 (October 2007): 1435–58. http://dx.doi.org/10.1216/rmjm/1194275928.

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44

Albuquerque, R. "WEIGHTED METRICS ON TANGENT SPHERE BUNDLES." Quarterly Journal of Mathematics 63, no. 2 (January 14, 2011): 259–73. http://dx.doi.org/10.1093/qmath/haq051.

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45

Boeckx, E., and L. Vanhecke. "Curvature homogeneous unit tangent sphere bundles." Publicationes Mathematicae Debrecen 53, no. 3-4 (October 1, 1998): 389–413. http://dx.doi.org/10.5486/pmd.1998.2071.

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Abbassi, Mohamed Tahar Kadaoui, Noura Amri, and Giovanni Calvaruso. "g ‐natural symmetries on tangent bundles." Mathematische Nachrichten 293, no. 10 (July 8, 2020): 1873–87. http://dx.doi.org/10.1002/mana.201900158.

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Kim, Jeong-Seop. "Bigness of the tangent bundles of projective bundles over curves." Comptes Rendus. Mathématique 361, G7 (October 24, 2023): 1115–22. http://dx.doi.org/10.5802/crmath.476.

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FEIX, BIRTE. "Hypercomplex manifolds and hyperholomorphic bundles." Mathematical Proceedings of the Cambridge Philosophical Society 133, no. 3 (November 2002): 443–57. http://dx.doi.org/10.1017/s0305004102006114.

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Using twistor techniques we shall show that there is a hypercomplex structure in the neighbourhood of the zero section of the tangent bundle TX of any complex manifold X with a real-analytic torsion-free connection compatible with the complex structure whose curvature is of type (1, 1). The zero section is totally geodesic and the Obata connection restricts to the given connection on the zero section.We also prove an analogous result for vector bundles: any vector bundle with real-analytic connection whose curvature is of type (1, 1) over X can be extended to a hyperholomorphic bundle over a neighbourhood of the zero section of TX.

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ALVAREZ, SÉBASTIEN. "Gibbs measures for foliated bundles with negatively curved leaves." Ergodic Theory and Dynamical Systems 38, no. 4 (December 15, 2016): 1238–88. http://dx.doi.org/10.1017/etds.2016.76.

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In this paper we develop a notion of Gibbs measure for the geodesic flow tangent to a foliated bundle over a compact negatively curved base. We also develop a notion of$F$-harmonic measure and prove that there exists a natural bijective correspondence between these two concepts. For projective foliated bundles with$\mathbb{C}\mathbb{P}^{1}$-fibers without transverse invariant measure, we show the uniqueness of these measures for any Hölder potential on the base. In that case we also prove that$F$-harmonic measures are realized as weighted limits of large balls tangent to the leaves and that their conditional measures on the fibers are limits of weighted averages on the orbits of the holonomy group.

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Khan, Mohammad. "Liftings from a para-Sasakian manifold to its tangent bundles." Filomat 37, no. 20 (2023): 6727–40. http://dx.doi.org/10.2298/fil2320727k.

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The purpose of the present paper is to study the liftings of a quarter symmetric non-metric connection from a para-Sasakian manifold to its tangent bundles. By liftings, some results of the curvature tensor, projective curvature tensor, concircular curvature tensor and conformal curvature tensor wrt a quarter symmetric non-metric connection in a P-Sasakian manifold to its tangent bundles are obtained.

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