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arXiv · 1808.06995

Sharp systolic inequalities for Riemannian and Finsler spheres of revolution

Alberto Abbondandolo·Barney Bramham·Umberto L. Hryniewicz·Pedro A. S. Salomão
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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.

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Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz, Pedro A. S. Salomão. 2018-08-21. Sharp systolic inequalities for Riemannian and Finsler spheres of revolution. https://arxiv.org/abs/1808.06995

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