Locally extremal geodesic loops on Riemannian manifold

José Luis Flores

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arXiv · 1709.07614

Locally extremal geodesic loops on Riemannian manifold

José Luis Flores

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Abstract

This note proves that any locally extremal non-self-conjugate geodesic loop in a Riemannian manifold is a closed geodesic. As a consequence, any complete and non-contractible Riemannian manifold with diverging injectivity radii along diverging sequences and without points conjugate to themselves, possesses a minimizing closed geodesic.

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José Luis Flores. 2017-09-22. Locally extremal geodesic loops on Riemannian manifold. https://arxiv.org/abs/1709.07614

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