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Sharp systolic inequalities for invariant tight contact forms on principal S1-bundles over S2 (2403.02228v3)

Published 4 Mar 2024 in math.SG, math.DG, and math.DS

Abstract: The systole of a contact form $\alpha$ is defined as the shortest period of closed Reeb orbits of $\alpha$. Given a non-trivial $\mathbb S1$-principal bundle over $\mathbb S2$ with total space $M$, we prove a sharp systolic inequality for the class of tight contact form on $M$ invariant under the $\mathbb S1$-action. This inequality exhibits a behavior which depends on the Euler class of the bundle in a subtle way. As applications, we prove a sharp systolic inequality for rotationally symmetric Finsler metrics on $\mathbb S2$, a systolic inequality for the shortest contractible closed Reeb orbit, and a particular case of a conjecture by Viterbo.

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Authors (1)

  1. Simon Vialaret
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