11 papers · 1 filter
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.…
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…
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…
Projectively Flat Finsler Metrics of Constant Curvature
Zhongmin Shen
It is the Hilbert's Fourth Problem to characterize the (not-necessarily-reversible) distance functions on a bounded convex domain in R^n such that straight lines are shortest paths…
Two-dimensional Finsler metrics of constant curvature
Zhongmin Shen
A Riemannian metric is of constant curvature if and only if it is locally projectively flat. There are infinitely many locally projectively flat Finsler metrics of constant curvatu…
Finsler Metrics with K=0 and S=0
Zhongmin Shen
In Finsler geometry, there are infinitely many models of constant curvature. The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are projectively flat with non-zero…