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Some curvature properties of spherically symmetric Finsler metrics.
- Source :
-
International Journal of Mathematics . Mar2024, Vol. 35 Issue 3, p1-17. 17p. - Publication Year :
- 2024
-
Abstract
- In this paper, we study some important Remannian and non-Riemannian curvature properties of spherically symmetric Finsler metrics. Under a condition on the geodesic coefficient, we find the necessary and sufficient conditions under which spherically symmetric metrics are of scalar flag curvature, W -quadratic or projectively Ricci-flat. For spherically symmetric metrics of relatively isotropic Landsberg curvature, we find the necessary and sufficient conditions under which these metrics are of constant flag curvature or Ricci-quadratic. Finally, we prove a rigidity result that every spherically symmetric metric of relatively isotropic Landsberg curvature is Ricci-quadratic if and only if it is a Berwald metric. Moreover, if the Finsler metric is negatively complete then it reduces to a Riemannian metric. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CURVATURE
*RIEMANNIAN metric
*GEODESICS
Subjects
Details
- Language :
- English
- ISSN :
- 0129167X
- Volume :
- 35
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- International Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176387624
- Full Text :
- https://doi.org/10.1142/S0129167X24500095