Sharp systolic inequalities for Riemannian and Finsler spheres of revolution

Trans. Amer. Math. Soc. 374 (2021), 1815-1845 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 shifti...

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Bibliographic Details
Main Authors:	Abbondandolo, Alberto, Bramham, Barney, Hryniewicz, Umberto L, Salomão, Pedro A. S
Format:	Journal Article
Language:	English
Published:	21-08-2018
Subjects:	Mathematics - Differential Geometry Mathematics - Dynamical Systems Mathematics - Symplectic Geometry
Online Access:	Get full text
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Summary:	Trans. Amer. Math. Soc. 374 (2021), 1815-1845 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.
DOI:	10.48550/arxiv.1808.06995