Locally extremal geodesic loops on a Riemannian manifold

Flores, José

doi:10.1090/proc/14046

Locally extremal geodesic loops on a Riemannian manifold
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by José Luis Flores

Proc. Amer. Math. Soc. 146 (2018), 4029-4033

DOI: https://doi.org/10.1090/proc/14046

Published electronically: June 11, 2018

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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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