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arXiv · 1707.00257

Closed geodesics with local homology in maximal degree on non-compact manifolds

Luca Asselle·Marco Mazzucchelli
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Abstract

We show that, on a complete and possibly non-compact Riemannian manifold of dimension at least 2 without close conjugate points at infinity, the existence of a closed geodesic with local homology in maximal degree and maximal index growth under iteration forces the existence of infinitely many closed geodesics. For closed manifolds, this was a theorem due to Hingston.

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Luca Asselle, Marco Mazzucchelli. 2017-07-02. Closed geodesics with local homology in maximal degree on non-compact manifolds. https://doi.org/10.1016/j.difgeo.2017.11.007

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