A conclusive theorem on Finsler metrics of sectional flag curvature

2018/12/22 by Libing Huang, Zhongmin Shen, Huang, Libing +1
Physics and Astronomy · #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.1812.09608

Abstract

If the flag curvature of a Finsler manifold reduces to sectional curvature, then locally either the Finsler metric is Riemannian, or the flag curvature is isotropic.

Related

• On the flag curvature of Finsler metrics of scalar curvature
• Finsler manifolds with Positive Weighted Flag Curvature
• Finsler Manifolds with Nonpositive Flag Curvature and Constant S-curvature
• Matsumoto metrics of constant flag curvature are trivial
• Reversible homogeneous Finsler metrics with positive flag curvature