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On $S$ -curvature of a homogeneous Finsler space with square metric

Gauree Shanker

Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab-151 001, India

E-mail Address: grshnkr2007@gmail.com

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and

Sarita Rani

http://orcid.org/0000-0002-7908-3106

Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab-151 001, India

E-mail Address: saritas.ss92@gmail.com

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https://doi.org/10.1142/S021988782050019XCited by:1 (Source: Crossref)

Abstract

The study of curvature properties of homogeneous Finsler spaces with $(α, β)$ -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 $(α, β)$ -metric is calculated.

Keywords:

AMSC: 22E60, 53C30, 53C60

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