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arXiv · 1302.3271

Generalized Isotropic Berwald Manifolds

A. Tayebi·E. Peyghan
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Abstract

In this paper, we construct a new class of Finsler manifolds called generalized isotropic Berwald manifolds which is an extension of the class of isotropic Berwald manifolds. We prove that every generalized isotropic Berwald manifold is a generalized Douglas-Weyl manifold. On a compact generalized isotropic Berwald manifold, we show that the notions of stretch and Landsberg curvatures are equivalent. Then we prove that on these manifolds, a Finsler metric is R-quadratic if and only if it is a stretch metric with vanishing E -curvature. Finally, we determine the flag curvature of generalized isotropic Berwald manifold with scalar flag curvature.

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A. Tayebi, E. Peyghan. 2013-02-12. Generalized Isotropic Berwald Manifolds. https://arxiv.org/abs/1302.3271

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