ON THE EXISTENCE OF INFINITELY MANY CLOSED GEODESICS ON NON-COMPACT MANIFOLDS

被引：6

作者：

Asselle, Luca ^{[1
]}

Mazzucchelli, Marco ^{[2
]}

机构：

[1] Ruhr Univ Bochum, Fak Math, Gebaude NA 4-33, D-44801 Bochum, Germany

[2] UMPA, Ecole Normale Super Lyon, CNRS, F-69364 Lyon 07, France

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 06期

关键词：

Closed geodesics; Morse theory; free loop space; COMPACT RIEMANNIAN-MANIFOLDS; SURFACES; POINTS; CURVES;

D O I：

10.1090/proc/13398

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that any complete (and possibly non-compact) Riemannian manifold M possesses infinitely many closed geodesics provided its free loop space has unbounded Betti numbers in degrees larger than dim(M) and there are no close conjugate points at infinity. Our argument builds on an existence result due to Benci and Giannoni and generalizes the celebrated theorem of Gromoll and Meyer for closed manifolds.

引用

页码：2689 / 2697

页数：9

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