A compactness theorem in Finsler geometry
Differential Geometry
2013-04-11 v1
Abstract
Let (M.F) be a complete Finsler manifold and P be a minimal and compact submanifold of M. Ric_k(x), x in M is a differential invariant that interpolates between the flag curvature and the Ricci curvature. We prove that if on any geodesic c(t) emanating orthogonally from P we have \int_{0}^{\infty}\mathbf{Ric}_{k}(t)>0, then M is compact.
Cite
@article{arxiv.1304.2937,
title = {A compactness theorem in Finsler geometry},
author = {Mihai Anastasiei and Ioan Radu Peter},
journal= {arXiv preprint arXiv:1304.2937},
year = {2013}
}
Comments
12 pages, no figures