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arXiv · 2005.10546

Homologically visible closed geodesics on complete surfaces

Simon Allais·Tobias Soethe
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Abstract

In this article, we give multiple situations when having one or two geometrically distinct closed geodesics on a complete Riemannian cylinder $M\simeq S^1\times\mathbb{R}$ or a complete Riemannian plane $M\simeq\mathbb{R}^2$ leads to having infinitely many geometrically distinct closed geodesics. In particular, we prove that any complete cylinder with isolated closed geodesics has zero, one or infinitely many homologically visible closed geodesics; this answers a question of Alberto Abbondandolo.

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Simon Allais, Tobias Soethe. 2020-05-21. Homologically visible closed geodesics on complete surfaces. https://doi.org/10.1142/s1793525321500692

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