Locally extremal geodesic loops on Riemannian manifold
Differential Geometry
2017-09-25 v1
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.
Cite
@article{arxiv.1709.07614,
title = {Locally extremal geodesic loops on Riemannian manifold},
author = {José Luis Flores},
journal= {arXiv preprint arXiv:1709.07614},
year = {2017}
}
Comments
5 pages