完整曲面上同调可见的闭测地线
Homologically visible closed geodesics on complete surfaces
摘要：
在这篇文章中，我们给出了多种情况下，有一个或两个几何不同的闭测地线上的一个完整的黎曼圆柱$M\simeq S^1\times\mathbb{R}$或一个完整的黎曼平面$M\simeq\mathbb{R}^2$导致有无穷多个几何不同的闭测地线。特别是，我们证明了任何完整的圆柱孤立闭测地线有零，一个或无穷多个同调可见的闭测地线，这回答了一个问题的阿尔贝托Abbondandolo。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
