Splitting theorems for Finsler manifolds of nonnegative Ricci curvature

Shin-ichi Ohta

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arXiv · 1203.0079

Splitting theorems for Finsler manifolds of nonnegative Ricci curvature

Shin-ichi Ohta

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Abstract

We investigate the structure of a Finsler manifold of nonnegative weighted Ricci curvature including a straight line, and extend the classical Cheeger-Gromoll-Lichnerowicz splitting theorem. Such a space admits a diffeomorphic, measure-preserving splitting in general. As for a special class of Berwald spaces, we can perform the isometric splitting in the sense that there is a one-parameter family of isometries generated from the gradient vector field of the Busemann function. A Betti number estimate is also given for Berwald spaces.

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Shin-ichi Ohta. 2012-03-01. Splitting theorems for Finsler manifolds of nonnegative Ricci curvature. https://arxiv.org/abs/1203.0079

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