Finsler Manifolds with Nonpositive Flag Curvature and Constant S-curvature
Differential Geometry
2007-05-23 v1 Metric Geometry
Abstract
The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an open subset in R^n with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler metric with negative flag curvature and constant S-curvature must be Riemannian if the manifold is compact. We also study the nonpositive flag curvature case.
Cite
@article{arxiv.math/0311232,
title = {Finsler Manifolds with Nonpositive Flag Curvature and Constant S-curvature},
author = {Zhongmin Shen},
journal= {arXiv preprint arXiv:math/0311232},
year = {2007}
}
Comments
15 pages