Finsler manifolds with nonpositive flag curvature and constant S-curvature

By Zhongmin Shen. 2003

53 citations recorded by the source corpus.

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 Rn 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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/e025c5ad3353c6ac9924ada856b0c3bddf2d9004

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In Astronomy and Astrophysics

1. A. Tayebi
2. Hao Xing
3. Benling Li
4. H. Sadeghi
5. Zhongmin Shen
6. Shin-ichi Ohta
7. H. Rademacher
8. Xinyue Cheng

Citations in the corpus

• On a class of weak Landsberg metrics (2007, background): “For example, for a closed Finsler manifold of nonpositive flag curvature, if the S-curvature is a constant, then it is weakly Landsbergian [10].”
• On generalized Douglas–Weyl (α, β)-metrics (2015, background): “(22) Since F is not Riemannian, then (1− F−2α2) 6= 0.”
• On Randers metrics with isotropic S-curvature (2008, background): “It is a non-Riemannian quantity which interacts with the flag curvature in a delicate way [5] [10] [19].”