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On Riemannian and Ricci curvatures of homogeneous Finsler manifolds
Published online by Cambridge University Press: 25 November 2024
Abstract
The famous Cheng-Shen’s conjecture in Riemann-Finsler geometry claims that every n-dimensional closed W-quadratic Randers manifold is a Berwald manifold. In this paper, first we study the Riemann and Ricci curvatures of homogeneous Finsler manifolds and obtain some rigidity theorems. Then, by using this investigation, we construct a family of W-quadratic Randers metrics which are not R-quadratic nor strongly Ricci-quadratic.
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society
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