Homologically visible closed geodesics on complete surfaces

Journal of Topology and Analysis, vol. 16, pp. 181–203

Abstract

In this paper, we give multiple situations when having one or two geometrically distinct closed geodesics on a complete Riemannian cylinder, a complete Möbius band or a complete Riemannian plane 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.

Authors 2

1. Simon Allais

   Université Paris Cité · Institut de Mathématiques de Jussieu-Paris Rive Gauche

   Affiliation as printed

   Université de Paris, IMJ-PRG, 8 Place Aurélie de Nemours, 75013 Paris, France

2. Tobias Soethe Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen, Fachgruppe Mathematik, Jakobstr 2, 52064 Aachen, Germany