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Keywords = homogeneous Finsler space

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13 pages, 302 KiB  
Article
On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space
by Yanlin Li, Manish Kumar Gupta, Suman Sharma and Sudhakar Kumar Chaubey
Mathematics 2023, 11(15), 3365; https://doi.org/10.3390/math11153365 - 1 Aug 2023
Cited by 22 | Viewed by 1429
Abstract
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 [...] Read more.
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. Full article
11 pages, 301 KiB  
Article
Curvatures on Homogeneous Generalized Matsumoto Space
by M. K. Gupta, Suman Sharma, Fatemah Mofarreh and Sudhakar Kumar Chaubey
Mathematics 2023, 11(6), 1316; https://doi.org/10.3390/math11061316 - 9 Mar 2023
Cited by 2 | Viewed by 1523
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Geometry of Manifolds and Applications)
5 pages, 236 KiB  
Article
The Existence of Two Homogeneous Geodesics in Finsler Geometry
by Zdeněk Dušek
Symmetry 2019, 11(7), 850; https://doi.org/10.3390/sym11070850 - 1 Jul 2019
Cited by 1 | Viewed by 2262
Abstract
The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler [...] Read more.
The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler manifold is proved. In a previous paper, examples of Randers metrics which admit just two homogeneous geodesics were constructed, which shows that the present result is the best possible. Full article
(This article belongs to the Special Issue Geometry of Submanifolds and Homogeneous Spaces)
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