Three dimensional manifolds all of whose geodesics are closed

TL;DR

This paper explores the Morse Theory of the energy function on the free loop space of the three sphere with metrics where all geodesics are closed, relating findings to the Berger Conjecture in three dimensions.

Contribution

It provides new insights into the Morse Theory of closed geodesics on the three sphere and connects these results to the Berger Conjecture.

Findings

Results on Morse Theory for closed geodesics

Connections to the Berger Conjecture in dimension three

Insights into the structure of three-dimensional manifolds with all geodesics closed

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.