Three-dimensional manifolds all of whose geodesics are closed
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.
KeywordsBerger conjecture Morse theory Manifolds all of whose geodesics are closed Three sphere
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- 1.Besse A.L.: Manifolds All of Whose Geodesics are Closed, volume 93 of Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas]. Springer, Berlin (1978)Google Scholar
- 2.Bökstedt M., Ottosen I.: The suspended free loop space of a symmetric space. Preprint Aarhus University 1(18), 1–31 (2004)Google Scholar
- 6.Gromoll, D., Grove, K.: On metrics on S 2 all of whose geodesics are closed. Invent. Math 65(1), 175–177 (1981/1982)Google Scholar