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Journal articles on the topic 'Berwald space'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

WU, WEISHENG. "Higher rank rigidity for Berwald spaces." Ergodic Theory and Dynamical Systems 40, no. 7 (2018): 1991–2016. http://dx.doi.org/10.1017/etds.2018.130.

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We generalize the higher rank rigidity theorem to a class of Finsler spaces, i.e. Berwald spaces. More precisely, we prove that a complete connected Berwald space of finite volume and bounded non-positive flag curvature with rank at least two whose universal cover is irreducible is a locally symmetric space or a locally Minkowski space.

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2

Shanker, Gauree. "Four-dimensional Conformally Flat Berwald and Landsberg Spaces." Journal of the Indian Mathematical Society 85, no. 1-2 (2018): 241. http://dx.doi.org/10.18311/jims/2018/14930.

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The problem of conformal transformation and conformal flatness of Finsler spaces has been studied in [6], [16], [17], [20], [21]. Recently, Prasad et. al [19] have studied three dimensional conformally flat Landsberg and Berwald spaces and have obtained some important results. The purpose of the present paper is to extend the idea of conformal change to four dimensional Finsler spaces and find the suitable conditions under which a four dimensional conformally at Landsberg space becomes a Berwald space.

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3

Mishra, Meera, and R. K. Pandey. "On Randers Change of a Generalized Exponential Metric." InPrime: Indonesian Journal of Pure and Applied Mathematics 6, no. 2 (2024): 194–204. https://doi.org/10.15408/inprime.v6i2.40885.

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In this paper, we study the properties of a special (α, β)-metric e^(k1β/α)+βe^(k2*β/α), the Randers change of the generalized exponential metric. We find the necessary and sufficient condition for this metric to be locally projectively flat and we also prove the conditions for this metric to be of the Berwald and Douglas type.Keywords: Berwald space; Douglas space; Finsler space; -metric; projectively flat. AbstrakPada artikel ini akan dipelajari sifat-sifat khusus dari (α, β) -metric e^(k1β/α)+βe^(k2*β/α), perubahan Randers dari metrik eksponensial umum. Kami menemukan syarat perlu dan cukup

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4

Torrome, Ricardo Gallego. "Average structures associated to a Finsler space." Annals of the Alexandru Ioan Cuza University - Mathematics 70, no. 2 (2024): 133–56. https://doi.org/10.47743/anstim.2024.00010.

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Given a Finsler space (M, F ) on a manifold M , the averaging method associates to Finslerian geometric objects affine geometric objects living on M . In particular, a Riemannian metric is associated with the fundamental tensor g and an affine, torsion free connection is associated with the Chern-Rund connection. As an illustration of the applications of theory, a generalization of the Gauss-Bonnet theorem to Berwald surfaces using the average metric is presented. The parallel transport and curvature endomorphisms of the average connection are obtained. The holonomy group for a Berwald space i

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5

Ramesha, Maranna, та S. K. Narasimhamurthy. "Projectively Flat Finsler Space of Douglas Type with Weakly-Berwald (α,β)-Metric". International Journal of Pure Mathematical Sciences 18 (серпень 2017): 1–12. http://dx.doi.org/10.18052/www.scipress.com/ijpms.18.1.

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The present article is organized as follows: In the first part, we characterize the important class of special Finsler (α,β)-metric in the form ofL=α+α2/β, whereαis Riemannian metric andβis differential 1-form to be projectively flat. In the second part, we describe condition for a Finsler spaceFnwith an (α,β)-metric is of Douglas type. Further we investigate the necessary and sufficient condition for a Finsler space with an (α,β)-metric to be weakly-Berwald space and Berwald space.

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6

Al-Qashbari, Adel Mohammed Ali. "On generalized for curvature Tensor \(P_{jkh}^i\) of second order in Finsler space." University of Aden Journal of Natural and Applied Sciences 24, no. 1 (2022): 171–76. http://dx.doi.org/10.47372/uajnas.2020.n1.a14.

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In this present paper, we introduced a Finsler space \(F_n\) which Cartan’s second curvature tensor \(P_{jkh}^i\) satisfies the generalized birecurrence property with respect to Berwald’s connection parameters \(G_{kh}^i\) which given by the condition\(B_n B_m P_{jkh}^i = a_{mn} P_{jkh}^i + b_{mn} ( δ_h^i g_{jk} - δ_k^i g_jh ) - 2 μ_m B_r (δ_h^i C_{jkn} - δ_k^i C_{jhn} ) y^r ,P_jkh^i≠0,\)where \(B_n B_m\) is Berwald’ scovariant differential of second order with respect to \(x^m\) and \(x^n\), successively, \(μ_m\) is non-zero covariant vector field, \(a_{mn}\) and \(b_{mn}\) are non-zero recur

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7

Alhamadi, Khaled M., Fahmi Yaseen Qasem, and Meqdad Ahmed Ali. "Different types of decomposition for certain tensors in \(K^h-BR-F_n\) and \(K^h-BR\)-affinely connected space." University of Aden Journal of Natural and Applied Sciences 20, no. 2 (2016): 355–63. http://dx.doi.org/10.47372/uajnas.2016.n2.a10.

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In this paper we defined \(K^h\)-birecurrent space which is characterized by the condition\(K_jkh|m|l^i=a_lm K_jkh^i\) , \(K_jkh^i≠0\), also we introduced some decompositions of Cartan's fourth and third curvature tensor and Berwald curvature tensor and its torsion tensor. The aim of this paper is devoted to the discussion of decomposition for different tensors in \(K^h\)-birecurrent space and \(K^h\)-birecurrent affinely connected space and the decomposition of curvature tensor Cartan's fourth and third in \(K^h\)-birecurrent space, also the decomposition of curvature tensor of Berwald in \(K

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8

Pandey, T. N., and V. K. Chaubey. "On Finsler Spaces with a Quartic Metric." Journal of the Tensor Society 2, no. 00 (2008): 37–47. http://dx.doi.org/10.56424/jts.v2i00.9958.

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The purpose of present paper is to study spaces with a quartic metric from the standpoint of Finsler Geometry. The Paper deals with Berwald and Landsberg spaces among quartic Finsler Spaces. A Finsler connections defined in a quartic Finsler space from the standpoint of the generalized metric spaces

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9

Asanov, G. S. "Finsleroid-regular space. Gravitational metric. Berwald case." Reports on Mathematical Physics 62, no. 1 (2008): 103–28. http://dx.doi.org/10.1016/s0034-4877(08)80037-7.

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10

Alaa, A. Abdallah, M. Al-Qashbari Adel, and M. Baleedi Saeedah. "Berwald Covariant Derivative and Lie Derivative of Conharmonic Curvature Tensors in Generalized Fifth Recurrent Finsler Space." GPH - International Journal of Mathematics 8, no. 01 (2025): 24–32. https://doi.org/10.5281/zenodo.14836508.

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This paper builds upon new define for the conharmonice curvature tensor in generaralized fifth recurrent Finsler space that Cartan’s fourth curvature tensor  in sense of Berwald <em>-</em>  via Lie derivative. We define a new conharmonic curvature tensor and explore its relationships with other established curvature tensors. Through various mathematical operations, including the Berwald covariant derivative and the Lie derivative, we derive new expressions for the conharmonic tensor and its interactions with other curvature tensors. The main results include the commutativity of

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11

Saleem, Abdalstar Ali Mohsen. "On a Generalized \(B_mU\) – Trirecurrent Finsler Space." University of Aden Journal of Natural and Applied Sciences 23, no. 2 (2019): 457–62. http://dx.doi.org/10.47372/uajnas.2019.n2.a15.

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A Finsler space \(F_{n}\) for which the h(v) - curvature tensor \(U_{jkh}^{i}\) satisfies the condition \(B_{m} U_{jkh}^{i}\)=\(λ_{m} U_{jkh}^{i}+μ_{m} (δ_{j}^{i} g_{kh}+δ_{k}^{i} g_{jh} )\), where \(λ_{m}\) and \(μ_{m}\) are non-zero covariant vector fields and \(B_{m}\) is covariant derivative of first order in the sense of Berwald (Berwald’s covariant differential operator). In the present paper, satisfying this condition will be called a generalized \(B_{m} U\)-recurrent space. The tensor \(G_{rkh}^{r}\), the h(v)-torsion tensor \(U_{kh}^{i}\), the G- Ricci tensor \(G_{jk}\) and the U- Ric

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12

Gupta, M. K., Suman Sharma, Fatemah Mofarreh, and Sudhakar Kumar Chaubey. "Curvatures on Homogeneous Generalized Matsumoto Space." Mathematics 11, no. 6 (2023): 1316. http://dx.doi.org/10.3390/math11061316.

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The curvature characteristics of particular classes of Finsler spaces, such as homogeneous Finsler spaces, are one of the major issues in Finsler geometry. In this paper, we have obtained the expression for S-curvature in homogeneous Finsler space with a generalized Matsumoto metric and demonstrated that the homogeneous generalized Matsumoto space with isotropic S-curvature has to vanish the S-curvature. We have also derived the expression for the mean Berwald curvature by using the formula of S-curvature.

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13

Qasem, Fahmi Yaseen Abdo. "Some types of generalized βH-Birecurrent Finsler space". University of Aden Journal of Natural and Applied Sciences 22, № 1 (2018): 159–66. http://dx.doi.org/10.47372/uajnas.2018.n1.a13.

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In this paper, we defined a Finsler space whose Berwald curvature tensor \(H_{jkh}^i\) satisfies the condition \(B_m B_n H_{jkh}^i= a_{mn} H_{jkh}^i+ b_{mn} (δ_k^i g_{jh}-δ_h^i g_{jk})-2y^r µ_nB_r (δ_k^i C_{jhm}-δ_h^i C_{jkm})\),where Bm Bn are Berwald covariant derivative of second order with respect to xm and xn, respectively, amn and bmn are non-zero covariant tensors field. The purpose of this paper is to develop the generalized βH-birecurrent space by studying some properties of generalized βH-birecurrent affinely connected space, P2-like generalized βH-birecurrent space and P*-generalize

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14

Pandey, P. N., and Manish Kumar Gupta. "On a four-dimensional Berwald space with vanishing h-connection vector $ k_i$." Tamkang Journal of Mathematics 39, no. 2 (2008): 121–30. http://dx.doi.org/10.5556/j.tkjm.39.2008.22.

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M. Matsumoto and R. Miron [2]$ ^{1)} $ constructed an orthonormal frame for an $ n $-dimensional Finsler space and the frame was called `Miron frame'. T. N. Pandey and D. K. Diwedi [3] and the present authors [4] studied four-dimensional Finsler spaces in terms of scalars. In the present paper, we study a four-dimensional Berwald space with vanishing $ h $-connection vector $ k_i $.

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15

Narasimhamurthy, S. K., G. N. Latha Kumari та C. S. Bagewadi. "Geometric Properties of Weakly Berwald Space with Some (α,β)-metric". Journal of the Tensor Society 5, № 01 (2007): 1–13. http://dx.doi.org/10.56424/jts.v5i01.10446.

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The (α,β)-metric is a Finsler metric which is contstructed from a Riemann- ian metric (α,β)and a di(α,β)erential 1-form ¯. In this paper Finsler space with some (α,β); ¯)-metrics like L = ((α,β) + ¯)2=(α,β) and L2 = 2(α,β)¯ becomes weakly Berwald spaces under some geometric and algebraic conditions.

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16

Qasem, Fahmi Yaseen Abdo, та Fatma Abdullah Mohammed Ahmed. "On a Generalized \(βH\) – Trirecurrent Finsler Space". University of Aden Journal of Natural and Applied Sciences 23, № 2 (2019): 463–67. http://dx.doi.org/10.47372/uajnas.2019.n2.a16.

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In this paper, we introduced a Finsler space for which the h - curvature tensor \(H_{jkh}^{i}\) (curvature tensor of Berwald) satisfies the condition\(β_{l} β_{m} β_{n} H_{jkh}^{i}=c_{lmn} H_{jkh}^{i}+d_{lmn} (δ_{k}^{i} g_{jh}-δ_{h}^{i} g_{jk} )-2y^{r} b_{mn} β_{r} (δ_{k}^{i} C_{jhl}-δ_{h}^{i} C_{jkl})\) \(-2y^{r} w_{ln} β_{r} (δ_{k}^{i} C_{jhm}-δ_{h}^{i} C_{jkm})-2y^{r} μ_{n} β_{l} β_{r} (δ_{k}^{i} C_{jhm}-δ_{h}^{i} C_{jkm}), H_{jkh}^{i}=0,\)where \(C_{jkm}\) is (h) hv - tortion tensor, \(β_{l} β_{m} β_{n}\) is Berwald's covariant differential operator of the third order with respect to \(x^{

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17

Xin, Li, and Chang Zhe. "Towards a gravitation theory in Berwald–Finsler space." Chinese Physics C 34, no. 1 (2010): 28–34. http://dx.doi.org/10.1088/1674-1137/34/1/005.

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18

Fuster, Andrea, Sjors Heefer, Christian Pfeifer, and Nicoleta Voicu. "On the Non Metrizability of Berwald Finsler Spacetimes." Universe 6, no. 5 (2020): 64. http://dx.doi.org/10.3390/universe6050064.

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We investigate whether Szabo’s metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern–Rund connection defines an affine connection on the underlying manifold), then it is affinely equivalent to a Riemann space, meaning that its affine connection is the Levi–Civita connection of some Riemannian metric. We show for the first time that this result does not extend to general Finsler spacetimes. More precisely, we find a large class of Berwal

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19

Tripathi, Brijesh, Sadika Khan та V. K. Chaubey. "On projectively flat Finsler space with a cubic (α, β) metric". Filomat 37, № 26 (2023): 8975–82. http://dx.doi.org/10.2298/fil2326975t.

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In the present paper, we have considered a cubic (?, ?) metric which is an special class of p-power Finsler metric, and obtained the conditions under which the Finsler space with such special metric will be projectively flat. Further, we also obtain in which case this Finsler space will be a Berwald space and Douglas space.

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20

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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21

Aldea, Nicoleta, and Gheorghe Munteanu. "Geometry of product complex Cartan manifolds." Analele Universitatii "Ovidius" Constanta - Seria Matematica 23, no. 1 (2015): 25–36. http://dx.doi.org/10.1515/auom-2015-0002.

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AbstractIn this paper we consider the product of two complex Cartan manifolds, the outcome being a class of product complex Cartan spaces. Then, we study the relationships between the geometric objects of a product complex Cartan space and its components, (e.g. Chern-Cartan complex nonlinear connection, Cartan tensors). By means of these, we establish the necessary and sufficient conditions under which a product complex Cartan space is Landsberg-Cartan or Berwald-Cartan or it has some other properties.

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22

Shanker, Gauree, and Kirandeep Kaur. "Homogeneous Finsler spaces with exponential metric." Advances in Geometry 20, no. 3 (2020): 391–400. http://dx.doi.org/10.1515/advgeom-2020-0008.

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AbstractWe prove the existence of an invariant vector field on a homogeneous Finsler space with exponential metric, and we derive an explicit formula for the S-curvature of a homogeneous Finsler space with exponential metric. Using this formula, we obtain a formula for the mean Berwald curvature of such a homogeneous Finsler space.

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23

Shanker, Gauree, and Sarita Rani. "On S-curvature of a homogeneous Finsler space with square metric." International Journal of Geometric Methods in Modern Physics 17, no. 02 (2020): 2050019. http://dx.doi.org/10.1142/s021988782050019x.

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The study of curvature properties of homogeneous Finsler spaces with [Formula: see text]-metrics is one of the central problems in Riemann–Finsler geometry. In this paper, the existence of invariant vector fields on a homogeneous Finsler space with square metric is proved. Further, an explicit formula for [Formula: see text]-curvature of a homogeneous Finsler space with square metric is established. Finally, using the formula of [Formula: see text]-curvature, the mean Berwald curvature of aforesaid [Formula: see text]-metric is calculated.

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24

ELGENDI, S. G. "ON THE PROBLEM OF NON-BERWALDIAN LANDSBERG SPACES." Bulletin of the Australian Mathematical Society 102, no. 2 (2020): 331–41. http://dx.doi.org/10.1017/s000497271900128x.

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We study the long-standing problem of the existence of non-Berwaldian Landsberg spaces from the perspective of conformal transformations. We calculate the Berwald and Landsberg tensors in terms of the T-tensor and show that there are Landsberg spaces with nonvanishing T-tensor. We give a necessary condition for a Landsberg space to be Berwaldian. We find conditions under which the Landsberg spaces cannot be Berwaldian and give examples of ($y$-local) non-Berwaldian Landsberg spaces.

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25

Natesh, N., S. K. Narasimhamurthy, and M.K. Roopa. "ON THE PROJECTIVE ALGEBRA OF MATSUMOTO SPACE." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 07 (2023): 3510–13. https://doi.org/10.5281/zenodo.8141421.

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In the present paper we are study of Matsumoto space on the projective algebra and Lie Algebra of the projective group. The projective Algebra of Matsumoto space is characterized as certain Lie sub algebra of the projective algebra. Further, which is devoted to studying the condition of Finsler space of constant flag curvature and vanishing S curvature admits a non Riemannian space of affine projective vector field with Matsumoto metric is Berwald space.

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26

Tabatabaeifar, Tayebeh, Behzad Najafi, and Mehdi Rafie-Rad. "On almost contact Finsler structures." International Journal of Geometric Methods in Modern Physics 17, no. 08 (2020): 2050126. http://dx.doi.org/10.1142/s0219887820501261.

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We introduce almost contact and cosymplectic Finsler manifolds. Then, we characterize almost contact Randers metrics. It is proved that a cosymplectic Finsler manifold of constant flag curvature must have vanishing flag curvature. We prove that every cosymplectic Finsler manifold is a Landsberg space, under a mild condition. Finally, we show that a cosymplectic Finsler manifold is a Douglas space if and only if it is a Berwald space.

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27

Ramesha, M., та K. Narasimhamurthy S. "Conformal Change of Finsler Special (α, β)-Metric is of Douglas Type". Journal of Progressive Research in Mathematics 8, № 1 (2016): 1220–26. https://doi.org/10.5281/zenodo.4028781.

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In this present article, we are devoted to study the necessary and sufficient conditions for a Finsler space with a special (𝛼, 𝛽)-Metric i.e., 𝐹 = 𝑐1𝛼 + 𝐶2𝛽 + 𝛽 2 𝛼 : 𝐶2 ≠ 0; to be a Douglas space and also to be Berwald space, where 𝛼 is Riemannian metric and 𝛽is differential 1-form. In the second part of this article we are discussing about conformal change of Douglas space with special (𝛼, 𝛽)-Metric metric.

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28

Lal, Chandra, та Prasad Yadav Ganga. "ON CONFORMAL TRANSFORMATION OF LAGRANGE SPACE WITH (Γ, Β)-METRIC". INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 09, № 02 (2021): 2178–86. https://doi.org/10.47191/ijmcr/v9i2.01.

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The present paper is a study of the conformal transformation of the Lagrange space with (γ, β)-metric. The conformal transformation of the spray coefficient and Riemann curvature are express in Lagrange space with (γ, β)-metric. Further, find out the condition that a conformal transformation of Lagrange space with (γ, β)-metric is locally dually flat if and only if the transformation is a homothety. Moreover, the conditions for the transform metrics to be Einstein and isotropic mean Berwald curvature are also find.

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29

Bácsó, S., and M. Matsumoto. "On Finsler spaces of Douglas type. A generalization of the notion of Berwald space." Publicationes Mathematicae Debrecen 51, no. 3-4 (1997): 385–406. http://dx.doi.org/10.5486/pmd.1997.1975.

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30

MOGHADDAM, HAMID REZA SALIMI. "ON THE RANDERS METRICS ON TWO-STEP HOMOGENEOUS NILMANIFOLDS OF DIMENSION FIVE." International Journal of Geometric Methods in Modern Physics 08, no. 03 (2011): 501–10. http://dx.doi.org/10.1142/s0219887811005257.

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In this paper we study the geometry of simply connected two-step nilpotent Lie groups of dimension five. We give the Levi–Civita connection, curvature tensor, sectional and scalar curvatures of these spaces and show that they have constant negative scalar curvature. Also we show that the only space which admits left-invariant Randers metric of Berwald type has three-dimensional center. In this case the explicit formula for computing flag curvature is obtained and it is shown that flag curvature and sectional curvature have the same sign.

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31

Deng, Shaoqiang, and Zhiguang Hu. "On Flag Curvature of Homogeneous Randers Spaces." Canadian Journal of Mathematics 65, no. 1 (2013): 66–81. http://dx.doi.org/10.4153/cjm-2012-004-6.

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AbstractIn this paper we give an explicit formula for the flag curvature of homogeneous Randers spaces of Douglas type and apply this formula to obtain some interesting results. We first deduce an explicit formula for the flag curvature of an arbitrary left invariant Randersmetric on a two-step nilpotent Lie group. Then we obtain a classification of negatively curved homogeneous Randers spaces of Douglas type. This results, in particular, in many examples of homogeneous non-Riemannian Finsler spaces with negative flag curvature. Finally, we prove a rigidity result that a homogeneous Randers sp

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32

Abdallah, Alaa A., Basel Hardan, Kirtiwant P. Ghadle, and AA Navlekar. "On generalized recurrent Finsler space of fifth order in Berwald sense." International Journal of Physics and Mathematics 6, no. 2 (2024): 29–35. http://dx.doi.org/10.33545/26648636.2024.v6.i2a.89.

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33

Kumar, Pradeep, T. S. Madhu та B. R. Sharath. "On Landsberg and Berwald Spaces of Two Dimensional Finslerian Space with Special (α, β)-Metric". OALib 06, № 03 (2019): 1–8. http://dx.doi.org/10.4236/oalib.1105244.

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34

Al-Qashbari, Adel M., Alaa A. Abdallah, and Saeedah M. Baleedi. "Projective Motions in Generalized Fifth Recurrent Finsler Space via Lie Derivative of Berwald Covariant Tensors." International Journal of Research Publication and Reviews 6, no. 4 (2025): 16101–6. https://doi.org/10.55248/gengpi.6.0425.16100.

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35

Shukla, H. S., Neelam Mishra та Vivek Shukla. "ON HYPERSURFACE OF THE FINSLER SPACE OBTAINED BY CONFORMAL β− CHANGE". Jnanabha 50, № 01 (2020): 49–56. http://dx.doi.org/10.58250/jnanabha.2020.50106.

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The conformal β− change of Finsler metric L(x, y) is given by L∗(x, y) = eσ(x) f (L(x, y), β(x, y)), where σ(x) is a function of x, β(x, y) = b i (x)yi is a one-form on the underlying manifold Mn , and f(L(x, y), β(x, y)) is a homogeneous function of degree one in L and β. Let Fn and F∗n be Finsler spaces with metric functions L and L∗ respectively. In this paper we study the hypersurface of F∗n and find condition under which this hypersurface becomes a hyperplane of first kind, a hyperplane of second kind and a hyperplane of third kind. In this endeavour we connect quantities of F∗n with thos

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36

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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37

Peyghan, Esmaeil, and Liviu Popescu. "Geometric structures on Finsler Lie algebroids and applications to optimal control." Filomat 36, no. 1 (2022): 39–71. http://dx.doi.org/10.2298/fil2201039p.

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In this paper some geometric structures on Finsler Lie algeboids are studied and h-basic distinguished connections are introduced. Specially, Ichijy? connection that is a special h-basic distinguished connection is investigated. The generalized Berwald Lie algebroids are presented, as a particular case of Finsler Lie algebroids and Wagner-Ichijy? connection, that is a special case of Ichijy? connection, is studied. Moreover, the Wagner Lie algebroid is introduced and some equivalent conditions for this space are given. Finally, an optimal control problem is solved using the Pontryagin Maximum

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Mylarappa, V. D., та N. S. Kampalappa. "THE STUDY OF BERWALD CONNECTION OF A FINSLER SPACE WITH A SPECIAL (α,β)-METRIC". Advances in Mathematics: Scientific Journal 9, № 6 (2020): 3221–28. http://dx.doi.org/10.37418/amsj.9.6.2.

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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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Harko, Tiberiu, Chor Yin Ho, Chun Sing Leung, and Stan Yip. "Jacobi stability analysis of the Lorenz system." International Journal of Geometric Methods in Modern Physics 12, no. 07 (2015): 1550081. http://dx.doi.org/10.1142/s0219887815500814.

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We perform the study of the stability of the Lorenz system by using the Jacobi stability analysis, or the Kosambi–Cartan–Chern (KCC) theory. The Lorenz model plays an important role for understanding hydrodynamic instabilities and the nature of the turbulence, also representing a nontrivial testing object for studying nonlinear effects. The KCC theory represents a powerful mathematical method for the analysis of dynamical systems. In this approach, we describe the evolution of the Lorenz system in geometric terms, by considering it as a geodesic in a Finsler space. By associating a nonlinear c

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WANAS, M. I. "AN AP-STRUCTURE WITH FINSLERIAN FLAVOR I: THE PRINCIPAL IDEA." Modern Physics Letters A 24, no. 22 (2009): 1749–62. http://dx.doi.org/10.1142/s0217732309030412.

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A geometric structure (FAP-structure), having both absolute parallelism and Finsler properties, is constructed. The building blocks of this structure are assumed to be functions of position and direction. A nonlinear connection emerges naturally and is defined in terms of the building blocks of the structure. Two linear connections, one of Berwald type and the other of the Cartan type, are defined using the nonlinear connection of the FAP. Both linear connections are nonsymmetric and consequently admit torsion. A metric tensor is defined in terms of the building blocks of the structure. The co

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Adel M. Al-Qashbari and Saeedah M. Baleedi. "A study of the concircular curvature tensor and its interactions with other tensors under the Lie derivative in \(GBK- 5RF_n\)." University of Aden Journal of Natural and Applied Sciences 28, no. 2 (2025): 89–96. https://doi.org/10.47372/uajnas.2024.n2.a08.

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This research paper delves into a comprehensive analysis of the concircular curvature tensor and its intricate relationships with other tensors under the Lie derivative. The concircular curvature tensor, a fundamental geometric invariant, plays a pivotal role in characterizing the local geometry of Riemannian manifolds. By employing the powerful tool of the Lie derivative, we explore how the concircular curvature tensor transforms under infinitesimal transformations of the underlying manifold. Our study uncovers novel connections between the concircular curvature tensor and other significant t

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Gupta, M. K., Abha Sahu, C. K. Yadav, Anjali Goswami, and Chetan Swarup. "KCC Theory of the Oregonator Model for Belousov-Zhabotinsky Reaction." Axioms 12, no. 12 (2023): 1133. http://dx.doi.org/10.3390/axioms12121133.

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The behavior of the simplest realistic Oregonator model of the BZ-reaction from the perspective of KCC theory has been investigated. In order to reduce the complexity of the model, we initially transformed the first-order differential equation of the Oregonator model into a system of second-order differential equations. In this approach, we describe the evolution of the Oregonator model in geometric terms, by considering it as a geodesic in a Finsler space. We have found five KCC invariants using the general expression of the nonlinear and Berwald connections. To understand the chaotic behavio

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Chang, Zhe, and Xin Li. "Modified Friedmann model in Randers–Finsler space of approximate Berwald type as a possible alternative to dark energy hypothesis." Physics Letters B 676, no. 4-5 (2009): 173–76. http://dx.doi.org/10.1016/j.physletb.2009.05.001.

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Blaga, Cristina, Paul Blaga, and Tiberiu Harko. "Jacobi and Lyapunov Stability Analysis of Circular Geodesics around a Spherically Symmetric Dilaton Black Hole." Symmetry 15, no. 2 (2023): 329. http://dx.doi.org/10.3390/sym15020329.

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We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing the space time of a charged black hole in the low energy limit of the string theory. The stability analysis is performed by using both the linear (Lyapunov) stability method, as well as the notion of Jacobi stability, based on the Kosambi–Cartan–Chern theory. Brief reviews of the two stability methods are also presented. After obtaining the geodesic equations in spherical symmetry, we reformulate them as a two-dimensional dynamic system. The Jacobi stability

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YOUSSEF, NABIL L., and A. M. SID-AHMED. "EXTENDED ABSOLUTE PARALLELISM GEOMETRY." International Journal of Geometric Methods in Modern Physics 05, no. 07 (2008): 1109–35. http://dx.doi.org/10.1142/s0219887808003235.

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In this paper, we study Absolute Parallelism (AP-) geometry on the tangent bundle TM of a manifold M. Accordingly, all geometric objects defined in this geometry are not only functions of the positional argument x, but also depend on the directional argument y. Moreover, many new geometric objects, which have no counterpart in the classical AP-geometry, emerge in this different framework. We refer to such a geometry as an Extended Absolute Parallelism (EAP-) geometry. The building blocks of the EAP-geometry are a nonlinear connection (assumed given a priori) and 2n linearly independent vector

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Bácsó, S., and R. Yoshikawa. "Weakly-Berwald spaces." Publicationes Mathematicae Debrecen 61, no. 1-2 (2002): 219–31. http://dx.doi.org/10.5486/pmd.2002.2741.

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Minguzzi, E. "The connections of pseudo-Finsler spaces." International Journal of Geometric Methods in Modern Physics 11, no. 07 (2014): 1460025. http://dx.doi.org/10.1142/s0219887814600251.

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We give an introduction to (pseudo-)Finsler geometry and its connections. For most results we provide short and self-contained proofs. Our study of the Berwald nonlinear connection is framed into the theory of connections over general fibered spaces pioneered by Mangiarotti, Modugno and other scholars. The main identities for the linear Finsler connection are presented in the general case, and then specialized to some notable cases like Berwald's, Cartan's or Chern–Rund's. In this way it becomes easy to compare them and see the advantages of one connection over the other. Since we introduce tw

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Crampin, Mike. "Invariant volumes, weakly-Berwald Finsler spaces, and the Landsberg--Berwald problem." Publicationes Mathematicae Debrecen 100, no. 1-2 (2022): 101–18. http://dx.doi.org/10.5486/pmd.2022.9060.

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Aldea, Nicoleta, and Gheorghe Munteanu. "On complex Landsberg and Berwald spaces." Journal of Geometry and Physics 62, no. 2 (2012): 368–80. http://dx.doi.org/10.1016/j.geomphys.2011.10.010.

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