Annals of Global Analysis and Geometry

, Volume 37, Issue 2, pp 173–184

Three-dimensional manifolds all of whose geodesics are closed

Original Paper

DOI: 10.1007/s10455-009-9180-x

Cite this article as:
Olsen, J. Ann Glob Anal Geom (2010) 37: 173. doi:10.1007/s10455-009-9180-x

Abstract

We present some results concerning the Morse Theory of the energy function on the free loop space of the three sphere for metrics all of whose geodesics are closed. We also explain how these results relate to the Berger conjecture in dimension three.

Keywords

Berger conjecture Morse theory Manifolds all of whose geodesics are closed Three sphere 

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA