论文标题
在完整表面上的同源可见的闭合大地测量学
Homologically visible closed geodesics on complete surfaces
论文作者
论文摘要
在本文中，我们给出多种情况，当在完整的Riemannian圆柱上拥有一个或两个几何截然不同的封闭地球学时，$ m \ simeq s^1 \ times \ times \ mathbb {r} $或完整的riemannian plane $ m \ m \ m \ simeq \ simeq \ simeq \ simeq {r}^2 $无限地与许多geodection in Dekodice Indentimelly geodice。特别是，我们证明了任何具有隔离闭合大地测量学的完整圆柱体的零，一个或无限的同源可见封闭的大地测量学；这回答了Alberto Abbondandolo的问题。
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.
