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Journal articles on the topic 'Finsler Space'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Prasad, B. N., T. N. Pandey, and Manoj Kumar Singh. "On Four Dimensional Finsler Space Satisfying T-Conditions." Journal of the Tensor Society 4, no. 01 (2007): 21–31. http://dx.doi.org/10.56424/jts.v4i01.10427.

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The purpose of the present paper is to consider the four dimensional Finsler spaces with Thijk = 0 and generalize the idea of Landsberg angle to four dimensional Finsler spaces. The properties of a Finsler space satisfying T−condition has been studied in a three dimensional Finsler space by various authors ([2], [3], [4], [8], [10]). But from the relativistic point of view the importance of four dimensional Finsler space is not negligible. In relativity the fourth coordinate is taken as time, from this point of view we discuss the properties of four dimensional Finsler space satisfying T−condi

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2

Al-Qashbari, Adel M., Alaa A. Abdallah та Kamal S. Nasr. "An Extension of Generalized 𝑼|𝒉−Birecurrent Finsler Space". International Journal of Mathematics and Statistics Invention 12, № 5 (2024): 21–25. http://dx.doi.org/10.35629/4767-12052125.

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This paper has focuses on a specific class of Finsler spaces known as generalized birecurrent Finsler space. By introducing a new geometric structure, we investigate the properties of these spaces and establish several theorems. Our results generalize previous work on birecurrent Finsler spaces and provide a deeper understanding of their geometry. In this paper, we introduced an extension of the generalized 𝑈−birecurrent Finsler spaces. i.e., we define a Finsler space 𝐹𝑛 which the curvature tensor 𝑈𝑗𝑘ℎ𝑖 satisfies the extension for generalized birecurrence property in sense of Cartan. Further,

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3

Qasem, Fahmi Yaseen Abdo, and Kamal Salem Naji Nasr. "Analysis for Cartan’s fourth curvature Tensor in Finsler space." University of Aden Journal of Natural and Applied Sciences 22, no. 2 (2018): 447–54. http://dx.doi.org/10.47372/uajnas.2018.n2.a17.

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In this paper we discussed decomposition for the curvature tensor \(K_{jkh}^i\) of three cases in generalized Kh–recurrent Finsler space, Kh–birecurrent Finsler space and Kh– trirecurrent Finsler space, some results have been obtained in such space, different identities concerning the above spaces.

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4

Mandal, Khageswar. "The Β-Change by Finsler Metric of C-Reducible Finsler Spaces in Finsler Geometry". Tribhuvan University Journal 33, № 1 (2019): 1–10. http://dx.doi.org/10.3126/tuj.v33i1.28674.

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This paper considered about the 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 and obtained the β-Change by Finsler metric of C-reducible Finsler spaces. Also further obtained the condition that a C-reducible Finsler space is transformed to a C-reducible Finsler space by a β-change of Finsler metric.

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5

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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6

Shanker, Gauree. "The L-dual of a Generalized m-Kropina Space." Journal of the Tensor Society 5, no. 01 (2007): 15–25. http://dx.doi.org/10.56424/jts.v5i01.10445.

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In 1987, R. Miron introduced the concept of L-duality between Cartan spaces and Finsler spaces ([5]) : The geometry of higher order Finsler spaces were sudied in ([1] ; [8]) : The theory of higher order Lagrange and Hamilton spaces were discussed in ([6] ; [7] ; [9]) : Some special problems concerning the L- duality and classes of Finsler spaces were studied in ([3] ; [13]) : In ([2] ; [10] ; [11]) the L-duals of Randers, Kropina and Matsumoto space were introduced. The L-dual of an (®; ¯) Finsler space was introduced in [12] :In this paper we give the L-dual of a generalized m-Kropina Space.

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7

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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8

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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9

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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10

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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11

Rastogi, S. C. "T3-Like Finsler Spaces." Journal of the Tensor Society 2, no. 00 (2008): 49–65. http://dx.doi.org/10.56424/jts.v2i00.9959.

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In 1972, T-tensor in a Finsler space of n- dimensions was introduced and studied simultaneously by H. Kawaguchi [3] and Matsumoto [5]. Several papers related with T-tensor , since then, have been published by various authors namely Hashiguchi [1] , Matsumoto [6]. Matsumoto and Shimada [7,8] , Rastogi [10,11] and others. The purpose of the present paper is to study some properties of T-tensor in a Finsler space of three dimensions. Furthermore, we have defined and studied Finsler spaces Fn, whose T-tensor is of special form and called them T3-like Finsler spaces

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12

DENG, SHAOQIANG, and ZIXIN HOU. "WEAKLY SYMMETRIC FINSLER SPACES." Communications in Contemporary Mathematics 12, no. 02 (2010): 309–23. http://dx.doi.org/10.1142/s0219199710003816.

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In this paper, we introduce the notion of weakly symmetric Finsler spaces and study some geometrical properties of such spaces. In particular, we prove that each maximal geodesic in a weakly symmetric Finsler space is the orbit of a one-parameter subgroup of the full isometric group. This implies that each weakly symmetric Finsler space has vanishing S-curvature. As an application of these results, we prove that there exist reversible non-Berwaldian Finsler metrics on the 3-dimensional sphere with vanishing S-curvature. This solves an open problem raised by Z. Shen.

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13

Yallappa Kumbar, Mallikarjun, Narasimhamurthy Senajji Kampalappa, Thippeswamy Komalobiah Rajanna та Kavyashree Ambale Rajegowda. "Killing Vector Fields in Generalized Conformalβ-Change of Finsler Spaces". Journal of Mathematics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/456291.

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We consider a Finsler space equipped with a Generalized Conformalβ-change of metric and study the Killing vector fields that correspond between the original Finsler space and the Finsler space equipped with Generalized Conformalβ-change of metric. We obtain necessary and sufficient condition for a vector field Killing in the original Finsler space to be Killing in the Finsler space equipped with Generalized Conformalβ-change of metric.

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14

XU, MING, and SHAOQIANG DENG. "KILLING FRAMES AND S-CURVATURE OF HOMOGENEOUS FINSLER SPACES." Glasgow Mathematical Journal 57, no. 2 (2014): 457–64. http://dx.doi.org/10.1017/s001708951400041x.

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AbstractIn this paper, we first deduce a formula of S-curvature of homogeneous Finsler spaces in terms of Killing vector fields. Then we prove that a homogeneous Finsler space has isotropic S-curvature if and only if it has vanishing S-curvature. In the special case that the homogeneous Finsler space is a Randers space, we give an explicit formula which coincides with the previous formula obtained by the second author using other methods.

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15

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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16

Pandey, P. N., and Suresh K. Shukla. "A Note on A±ne Motion in a Birecurrent Finsler Space." Journal of the Tensor Society 4, no. 01 (2007): 93–101. http://dx.doi.org/10.56424/jts.v4i01.10419.

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Several authors discussed a±ne motion generated by contra, concurrent, special concircular, recurrent, concircular and torse forming vector ¯elds in spe- cial spaces such as recurrent, birecurrent and symmetric Riemannian and Finsler spaces. The ¯rst author [20-22] for the ¯rst time obtained the necessary and su±cient conditions for the above vector ¯elds to generate an a±ne motion in a general Finsler space. Recently Surendra Pratap Singh [26] discussed a±ne motion in a birecurrent Finsler space. The aim of this paper is to generalize the results of Surendra Pratap Singh.

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17

Qasem, By: F. Y. A. "ON Rh -TRIRECURRENT FINSLER SPACES." Journal of the faculty of Education 1, no. 5 (2023): 57–74. http://dx.doi.org/10.60037/edu.v1i5.1207.

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The concept of recurrent curvature of an n-dimensional Riemannian space was extended to a Finsler space by A. Moór ([7], [8],[9]). Shalini Dikshit [3] defined the birecurrent Finsler space and F.Y.A.Qasem [10] defined the generalized birecurrent Finsler space and their properties considering the Cartan's curvature tensor i  jkh R x , y , y x& .The object of the present paper is to study trirecurrent Finsler space considering the Cartan's curvature tensor ikh R x , y .

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18

Pandey, T. N., та Suraj Kumar Shukla. "On Finsler Spaces Satisfying the Condition Lm+1C = γm". Journal of the Tensor Society 10, № 01 (2007): 41–48. http://dx.doi.org/10.56424/jts.v10i01.10575.

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In the year 1979, M. Matsumoto has discussed non-Riemannian Finsler spaces with vanishing T-Tensor. In the paper, M. Matsumoto has shown that if a Finsler space Mn satisfy T−condition i.e. Thijk = 0, Then for such a Finsler space the function L 2C 2 of Mn is a function of position only (i.e. L2C 2 = f(x)), where L is fundamental function and C 2 is the square of length of torsion tensor Ci. In continuity of the above paper F. Ikeda in the year 1984, studied Finsler spaces L 2C 2 as a function of x in detail. In the year 1991, Ikeda considered Finsler spaces satisfying the condition L 2C 2 as t

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19

Qasem, Fahmi Yaseen Abdo. "On Study Ch-Trirecurrent Finsler Space." Thamar University Journal of Natural & Applied Sciences 6, no. 6 (2023): 57–64. http://dx.doi.org/10.59167/tujnas.v6i6.1328.

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The concept of C^h- recurrent Finsler space has been studied by M.Matsumoto [6] . H.Izumi ([4],[5]) gave the concept of *P- spaces which was the generalization of C^h-recurrent spaces and P2-like spaces of M.Matsumoto ([6],[7]). R.Verma [15] discussed C^h- birecurrent spaces where these spaces are generalization of C^h- recurrent spaces of M.Matsumoto [6] .Besides the correlation of C^h- birecurrent spaces which C^h- recurrent space , some special C^h- birecurrent spaces has been discussed . The result concerning h- isotropic C^h- recurrent space due to M.Matsumoto [6] has been extended to C^h

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20

YOUSSEF, NABIL L., AMR M. SID-AHMED, and EBTSAM H. TAHA. "ON FINSLERIZED ABSOLUTE PARALLELISM SPACES." International Journal of Geometric Methods in Modern Physics 10, no. 07 (2013): 1350029. http://dx.doi.org/10.1142/s0219887813500291.

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The aim of this paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism (GAP)-space. The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized absolute parallelism (parallelizable) space, combines within its geometric structure the simplicity of GAP-geometry and the richness of Finsler geometry, hence is potentially more suitable for applications and especially for describing physical phenomena. A study of the geometry of the two stru

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21

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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22

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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23

Kumari, G. N. Latha, та S. K. Narasimhamurthy. "Douglas space of Second Kind of Finsler space with (α, β)−Metric". Journal of the Tensor Society 8, № 01 (2007): 93–102. http://dx.doi.org/10.56424/jts.v8i01.10555.

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The (α, β)-metric is a Finsler metric which is contstructed from a Riemannian metric α and a differential 1−form β. In this paper we discussed the conditions under which the Finsler space with (α, β)−metric L = β 2/(β − α) become a Douglas space of Second Kind.

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24

Al-Qashbari, Adel Mohammed Ali. "A Study of the M-Projective Curvature Tensor in Generalized Recurrent and Birecurrent Finsler Spaces." Journal of Science and Technology 30, no. 6 (2025): 87–86. https://doi.org/10.20428/jst.v30i6.2917.

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This paper aims to examine the properties of the M-projective curvature tensor in the context of generalized Finsler spaces, specifically within the framework of a -space. The study begins with the derivation of the M-projective curvature tensor, which is expressed as the sum of the standard M-projective curvature tensor and additional terms involving the Ricci tensor and scalar curvature. Through covariant differentiation, the behavior of this tensor under certain conditions is analyzed, leading to a set of conditions necessary for the space to exhibit generalized recurrent Finsler properties

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25

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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26

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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27

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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28

Kumar Mathur, Praveen, and Pravin Kumar Srivastava. "SPECIAL NORMAL AND NEO-NORMAL PROJECTIVE RECURRENT, BI-RECURRENT, FINSLER SPACES ADMITTING AFFINE MOTION." Jnanabha 52, no. 01 (2022): 134–40. http://dx.doi.org/10.58250/jnanabha.2022.52117.

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This paper deals with the study of the recurrent and bi-recurrent, Neo-normal / normal and special normal projective Finsler spaces admitting an affine motion. The relation between two Ricci tensors has been established in a normal projective Finsler space and in a special normal projective Finsler space, the recurrence tensor of a birecurrent vector field generating an affine motion can not be independent of the directional arguments and is always non-symmetric. Also, some special types of affine motion generated by a vector field whose covariant derivative is recurrent have been discussed in

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29

Prasad, B. N., T. N. Pandey, and Amitabh Mishra. "On P3-Like Finsler Space." Journal of the Tensor Society 1, no. 01 (2007): 51–61. http://dx.doi.org/10.56424/jts.v1i01.9948.

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There are three kinds of torsion tensor in Cartan’s theory of Finsler spaces. Two of them are (h) hv-torsion tensor Cijk and (v) hv-torsion tensor Pijk,which are symmetric in all their indices and both are indicatory tensors. Mathematics have studied various interesting special forms of these torsion tensors. For example C-reducible [2], semi C- reducible [6],C2-like [6] and C3-like[9] Finsler spaces are based on the special forms of Cijk where as P-reducible [1] [5] and P-symmetric [5] Finsler spaces are based on the special forms of Pijk. In the present paper we shall discuss another special

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30

Al-Qashbari, Adel M. A. "Recurrence Decompositions in Finsler Space." Journal of Mathematical Analysis and Modeling 1, no. 1 (2020): 77–86. http://dx.doi.org/10.48185/jmam.v1i1.40.

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Finsler geometry is a kind of differential geometry originated by P. Finsler. Indeed, Finsler geometry has several uses in a wide variety and it is playing an important role in differential geometry and applied mathematics of problems in physics relative, manual footprint. It is usually considered as a generalization of Riemannian geometry. In the present paper, we introduced some types of generalized $W^{h}$ -birecurrent Finsler space, generalized $W^{h}$ -birecurrent affinely connected space and we defined a Finsler space $F_{n}$ for Weyl's projective curvature tensor $W_{jkh}^{i}$ satisfies

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31

Qasem, Fahmi Yaseen, Adel Mohammed Al-Qashbari, and Mohsen Mohammed Husien. "On Generalized \(R^h\) -Trirecurrent Space." University of Aden Journal of Natural and Applied Sciences 24, no. 2 (2022): 475–80. http://dx.doi.org/10.47372/uajnas.2020.n2.a14.

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In the present paper‚ a Finsler space \(F_n\) whose Cartan’s fourth curvature tensor \(R_jkh^i\) satisfies \(R_{(jkh|l|m|n)}^i = c_{lmn} R_{jkh}^i + d_{lmn} ( δ_k^i g_{jh} - δ_h^i g_{jk} )\), \(R_jkh^i≠0\) , where \(c_{lmn}\) and \(d_{lmn}\) are non-zero covariant tensor fields, of third order is introduced and such space is called as generalized \(R^h\) -trirecurrent Finsler space and denote it briefly by \(GR^h-TRF_n\)‚ we obtained some generalized trirecurrent spaces. Also we introduced Ricci generalized trirecurrent space.

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32

Tiwari, Bankteshwar, and Manoj Kumar. "On Randers change of a Finsler space with mth-root metric." International Journal of Geometric Methods in Modern Physics 11, no. 10 (2014): 1450087. http://dx.doi.org/10.1142/s021988781450087x.

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In this paper, we find a condition under which a Finsler space with Randers change of mth-root metric is projectively related to a mth-root metric and also we find a condition under which this Randers transformed mth-root Finsler metric is locally dually flat. Moreover, if transformed Finsler metric is conformal to the mth-root Finsler metric, then we prove that both of them reduce to Riemannian metrics.

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33

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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34

Wu, Mengke, Xiaoling Zhang, Lingen Sun, and Lingyue Han. "Some Curvature Properties of Finsler Warped Product Metrics." Symmetry 15, no. 8 (2023): 1565. http://dx.doi.org/10.3390/sym15081565.

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The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space-time. In this paper, we first obtain the PDE characterization of Finsler warped product metrics with a vanishing Riemannian curvature. Moreover, we obtain equivalent conditions for locally Minkowski Finsler warped product spaces. Finally, we explicitly construct two types of non-Riemannian examples.

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35

Li, Yanlin, Manish Kumar Gupta, Suman Sharma, and Sudhakar Kumar Chaubey. "On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space." Mathematics 11, no. 15 (2023): 3365. http://dx.doi.org/10.3390/math11153365.

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The characterization of Finsler spaces with Ricci curvature is an ancient and cumbersome one. In this paper, we have derived an expression of Ricci curvature for the homogeneous generalized Matsumoto change. Moreover, we have deduced the expression of Ricci curvature for the aforementioned space with vanishing the S-curvature. These findings contribute significantly to understanding the complex nature of Finsler spaces and their curvature properties.

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36

Miyachi, Hideki, Ken'ichi Ohshika, and Athanase Papadopoulos. "Tangent spaces of the Teichmüller space of the torus with Thurston's weak metric." Annales Fennici Mathematici 47, no. 1 (2022): 325–34. http://dx.doi.org/10.54330/afm.113702.

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In this paper, we show that the analogue of Thurston's asymmetric metric on the Teichmüller space of flat structures on the torus is weak Finsler and we give a geometric description of its unit circle at each point in the tangent space to Teichmüller space. We then introduce a family of weak Finsler metrics which interpolate between Thurston's asymmetric metric and the Teichmüller metric of the torus (which coincides with the hyperbolic metric). We describe the unit tangent circles of the metrics in this family.

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37

Tiwari, S. K., and Shiv Prakash Mishra. "Affine Motion in a Finsler Space with Non-Symmetric Connections." Journal of the Tensor Society 3, no. 00 (2009): 119–24. http://dx.doi.org/10.56424/jts.v3i01.9976.

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Tokano [5] studied the affine motion and its properties in a recurrent Finsler space. Further, Pandey and Tiwari [3] developed the existence of affine motion in a R recurrent Finsler space equipped with non-symmetric connections. The object of the present paper is to study the infinitesimal affine motion in a Finsler space with non-symmetric connection. Some useful investigation have been obtained in the paper.

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38

Tiwari, S. K., and Shiv Prakash Mishra. "Affine Motion in a Finsler Space with Non-Symmetric Connections." Journal of the Tensor Society 3, no. 01 (2009): 119–24. http://dx.doi.org/10.56424/jts.v3i00.9976.

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Tokano [5] studied the affine motion and its properties in a recurrent Finsler space. Further, Pandey and Tiwari [3] developed the existence of affine motion in a R recurrent Finsler space equipped with non-symmetric connections. The object of the present paper is to study the infinitesimal affine motion in a Finsler space with non-symmetric connection. Some useful investigation have been obtained in the paper.

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39

Rinkal. "Reversible Geodesics of a Finsler Space with (α,β)-Metric". Advances in Nonlinear Variational Inequalities 28, № 2s (2024): 399–410. https://doi.org/10.52783/anvi.v28.2711.

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This paper deals with the existence of reversible geodesics over a Finsler space with some (α,β)-metrics. The conditions for a Finsler space (M,F) to be with reversible geodesics are obtained. We study some geometrical properties of F with reversible geodesics and prove that the Finsler metric F induces a weighted quasi-metric d_F on M.

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40

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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41

Xu, Ming, and Shaoqiang Deng. "Homogeneous Finsler spaces and the flag-wise positively curved condition." Forum Mathematicum 30, no. 6 (2018): 1521–37. http://dx.doi.org/10.1515/forum-2018-0130.

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Abstract In this paper, we introduce the flag-wise positively curved condition for Finsler spaces (the (FP) condition), which means that in each tangent plane, there exists a flag pole in this plane such that the corresponding flag has positive flag curvature. Applying the Killing navigation technique, we find a list of compact coset spaces admitting non-negatively curved homogeneous Finsler metrics satisfying the (FP) condition. Using a crucial technique we developed previously, we prove that most of these coset spaces cannot be endowed with positively curved homogeneous Finsler metrics. We a

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42

Rastogi, S. C. "On a vector filed analogous to concurrent vector field in a Finsler space." Journal of the Tensor Society 1, no. 01 (2007): 15–23. http://dx.doi.org/10.56424/jts.v1i01.9944.

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Concurrent vector fields in a Finsler space were first of all defined and studied by Tachibana [6], followed by Matsumoto [2] and others. Recently in 2004, Rastogi and Dwivedi [4] studied the existence of concurrent vector fields in a Finsler space of n-dimensional and showed that the definition in its present form is unsuitable. Further they gave a modified definition of a concurrent vector field in a Finsler space of a n-dimension.

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43

Stavrinos, Panayiotis C., and Maria Alexiou. "Raychaudhuri equation in the Finsler–Randers space-time and generalized scalar-tensor theories." International Journal of Geometric Methods in Modern Physics 15, no. 03 (2018): 1850039. http://dx.doi.org/10.1142/s0219887818500391.

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In this work, we obtain the Raychaudhuri equations for various types of Finsler spaces as the Finsler–Randers (FR) space-time and in a generalized geometrical structure of the space-time manifold which contains two fibers that represent two scalar fields [Formula: see text]. We also derive the Klein–Gordon equation for this model. In addition, the energy conditions are studied in a FR cosmology and are correlated with FRW model. Finally, we apply the Raychaudhuri equation for the model [Formula: see text], where M is a FRW-space-time.

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44

Tripathi, Brijesh Kumar, та Sadika Khan. "Flat-Parallel Minkowski Space and β-Change with α,β-Metric". Journal of Mathematics 2024 (22 травня 2024): 1–6. http://dx.doi.org/10.1155/2024/4122492.

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The purpose of this paper is to examine the condition for a Finsler space with a generalized α,β-metric to be projectively flat. In addition, we establish that the Finsler space with generalized α,β-metric is a flat-parallel Minkowski space and derive the condition under which the β-change for the aforementioned metric is projective. We also explored the projective nature of β-change for various significant Finsler metrics derived from the generalized α,β-metric.

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45

Miyan, Poonam, Hemlata Pande та Dhirendra Thakur. "On ϑ – Curvature Tensor of Finslerian Hypersurfaces Given by Generalised Kropina Type Metric". Nepal Journal of Mathematical Sciences 6, № 1 (2025): 1–6. https://doi.org/10.3126/njmathsci.v6i1.77368.

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The purpose of the present paper is to find angular metric tensor, carton torsion tensor, vcurvature tensor in a generalized Kropina space and the relation between v -curvatures with respect to Cartan connection CΓ of a Finsler space Fn = (Mn, L) and a Finsler space F*n = (Mn, L*) whose metric L* is derived from the metric L of Fn by L* (x, y) = μ1/2 (x, y) β1/2 (x, y), where μ1/2 (x, y) = (L1/2 + β1/2) (x, y) and β = bi(x) yi. The Finsler space F*n is called a generalized Kropina space under certain conditions.

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46

Sun, Lingen, Xiaoling Zhang, and Mengke Wu. "Finsler Warped Product Metrics with Special Curvature Properties." Axioms 12, no. 8 (2023): 784. http://dx.doi.org/10.3390/axioms12080784.

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The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space–time. In this paper, we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we find differential equations of Finsler warped product metrics with vanishing χ-curvature or vanishing H-curvature. Furthermore, we show that, for Finsler warped product metrics, the χ-curvature vanishes if and only if the H-curvature vanishes

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47

Narasimhamurthy, S. K., and D. M. Vasantha. "Ricci Flow Equations on Special Finsler Space." Journal of the Tensor Society 8, no. 01 (2007): 121–30. http://dx.doi.org/10.56424/jts.v8i01.10552.

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48

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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Tripathi, Brijesh Kumar, та K. B. Pandey. "On a Special Form of(h) hν-Torsion TensorPijkin Finsler Space". Journal of Mathematics 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/3694017.

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A special form of (h)hν-torsion tensor was introduced which may be considered generalization ofP⁎-Finsler space andP-reducible Finsler space and then some properties of this space were studied. We also introduce connection and give some case and condition of torsion tensorTjki.

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50

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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