On generalized Berwald R-quadratic metrics

Articles in Press

Document Type : Research Paper

Authors

1 department of mathematics, urmia university

2 Department of mathematics, Urmia University, Urmia , Iran

3 department of mathematics, qom university

10.22098/jhs.2025.16423.1065

Abstract

‎Every Riemannian metric is R-quadratic, while many Finsler metrics have not this property‎. ‎A Finsler metric is called R-quadratic if its Riemannian curvature is quadratic in all direction at any points of the underlying manifold‎. ‎A Finsler metric on a manifold is called a generalized Berwald metric if there exists a covariant derivative such that the parallel translations induced by it preserve the Finsler function‎. ‎In this paper‎, ‎we study the class of generalized Berwald (α, β)-manifolds with R-quadratic properties and prove a rigidity result‎. ‎We show that such manifolds satisfy S=0 if and only if B=0‎.

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References

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Journal of Hyperstructures

Articles in Press, Accepted Manuscript
Available Online from 09 July 2025

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