On Purely Hermitian R-complex Finsler Space with (α, β)-Metric

K. S. Venkatesha; S. K. Narasimhamurthy; K. Chandru

doi:10.22342/jims.27.2.929.240-248

K. S. Venkatesha ⁽¹⁾ , S. K. Narasimhamurthy ⁽²⁾ , K. Chandru ⁽³⁾

(1) Kuvempu University, India,

(2) Kuvempu University, India,

(3) Department of Mathematics, PESITM, Shivamoga, Karnataka, India

https://doi.org/10.22342/jims.27.2.929.240-248

Issue
VOLUME 27 NUMBER 2 (July 2021)

Submitted
May 29, 2020

Accepted
July 16, 2021

Published
July 24, 2021

Keywords:

R-complex Finsler space, Purely Hermitian metric, Connection coefficients, Berwald space

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Abstract

In the present paper we established some interesting results on purely Hermitian R-complex Finsler space with (α, β)-metrics, Firstly we characterize the conditions for the (α, β)-metric F = p α2 + εβ2 to be a purely Hermitian. Then determined the fundamental metric tensor, its inverse and determinent of the above metric. Further obtained Chern-Finsler connection coefficients and analysed necessary conditions under which an purely Hermitian R-complex Finsler space with (α, β)-metric to be Berwald, Kahler and strongly Kahler also given some examples.

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Authors

K. S. Venkatesha

Kuvempu University

S. K. Narasimhamurthy

Kuvempu University

https://orcid.org/0000-0002-2711-4636

nmurthysk@hotmail.com (Primary Contact)

K. Chandru

Department of Mathematics, PESITM, Shivamoga, Karnataka

Venkatesha, K. S., Narasimhamurthy, S. K., & Chandru, K. (2021). On Purely Hermitian R-complex Finsler Space with (α, β)-Metric. Journal of the Indonesian Mathematical Society, 27(2), 240–248. https://doi.org/10.22342/jims.27.2.929.240-248