Splitting theorems for Finsler manifolds of nonnegative Ricci curvature

Understand

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.