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math.DG2003
Finsler Manifolds with Nonpositive Flag Curvature and Constant S-curvature
Zhongmin Shen
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.…
math.DG2003
On the flag curvature of Finsler metrics of scalar curvature
Xinyue Chen, Xiaohuan Mo, Zhongmin Shen
The flag curvature of a Finsler metric is called a Riemannian quantity because it is an extension of sectional curvature in Riemannian geometry. In Finsler geometry, there are seve…
math.DG2003
On Negatively Curved Finsler Manifolds of Scalar Curvature
Xiaohuan Mo, Zhongmin Shen
In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n>2. We show that for such a Finsler manifold, if the fla…