Algebraic & Geometric Topology

On the multiplicity of isometry-invariant geodesics on product manifolds

Marco Mazzucchelli

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Abstract

We prove that on any closed Riemannian manifold (M1×M2,g), with dim(M2)2 and rankH1(M1)0, every isometry homotopic to the identity admits infinitely many isometry-invariant geodesics.

Article information

Source
Algebr. Geom. Topol., Volume 14, Number 1 (2014), 135-156.

Dates
Received: 14 May 2012
Revised: 28 July 2013
Accepted: 31 July 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715797

Digital Object Identifier
doi:10.2140/agt.2014.14.135

Mathematical Reviews number (MathSciNet)
MR3158756

Zentralblatt MATH identifier
1329.58005

Subjects
Primary: 58E10: Applications to the theory of geodesics (problems in one independent variable)
Secondary: 53C22: Geodesics [See also 58E10]

Keywords
isometry-invariant geodesics closed geodesics Morse theory

Citation

Mazzucchelli, Marco. On the multiplicity of isometry-invariant geodesics on product manifolds. Algebr. Geom. Topol. 14 (2014), no. 1, 135--156. doi:10.2140/agt.2014.14.135. https://projecteuclid.org/euclid.agt/1513715797


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