Department Of Mathematics And Statistics

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On CW-translations of homogeneous Finsler spaces with (?,?)-metrics
(Balkan Society of Geometers, 2021-03-01T00:00:00) Rani, S.; Shanker, G.
In the present paper, we consider homogeneous Finsler spaces with two (?,?)-metrics. Taking a Killing vector ?eld X on one of these spaces, we find necessary and su?cient conditions for X to be Killing on the other space. Further, by taking a Killing vector ?eld X of constant length on one of these spaces, we ?nd the condition under which the Killing vector ?led X has constant length w.r.t. other space also. Taking Killing vector ?elds of constant length, we ?nd CW translations on these spaces. � 2021 Balkan Society of Geometers, Geometry Balkan Press. All Rights Reserved.
On S -curvature of a homogeneous Finsler space with square metric
(World Scientific Publishing Co. Pte Ltd, 2020) Shanker G.; Rani S.
The study of curvature properties of homogeneous Finsler spaces with (?,?)-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 S-curvature of a homogeneous Finsler space with square metric is established. Finally, using the formula of S-curvature, the mean Berwald curvature of aforesaid (?,?)-metric is calculated.