Homogeneous Finsler sphere with constant flag curvature

Ming Xu

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arXiv · 1906.02942

Homogeneous Finsler sphere with constant flag curvature

Ming Xu

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Abstract

We prove that a homogeneous Finsler sphere with constant flag curvature $K\equiv1$ and a prime closed geodesic of length $2π$ must be Riemannian. This observation provides the evidence for the non-existence of homogeneous Bryant spheres. It also helps us propose an alternative approach proving that a geodesic orbit Finsler sphere with $K\equiv1$ must be Randers. Then we discuss the behavior of geodesics on a homogeneous Finsler sphere with $K\equiv1$. We prove that many geodesic properties for homogeneous Randers spheres with $K\equiv1$ can be generalized to the non-Randers case.

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BibTeX RIS

Ming Xu. 2019-06-12. Homogeneous Finsler sphere with constant flag curvature. https://arxiv.org/abs/1906.02942

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