Sharp systolic inequalities for Riemannian and Finsler spheres of revolution
Abstract
We prove that the systolic ratio of a sphere of revolution $S$ does not exceed $\pi$ and equals $\pi$ if and only if $S$ is Zoll. More generally, we consider the rotationally symmetric Finsler metrics on a sphere of revolution which are defined by shifting the tangent unit circles by a Killing vector field. We prove that in this class of metrics the systolic ratio does not exceed $\pi$ and equals $\pi$ if and only if the metric is Riemannian and Zoll.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.06995
- arXiv:
- arXiv:1808.06995
- Bibcode:
- 2018arXiv180806995A
- Keywords:
-
- Mathematics - Symplectic Geometry;
- Mathematics - Differential Geometry;
- Mathematics - Dynamical Systems;
- 53Dxx
- E-Print:
- 35 pages, 3 figures