We investigate the curvature and topology of Finsler manifolds, mainly the growth of the fundamental group. By choosing a new counting function for the fundamental group that does not rely on the generators, we are able to discuss the topic in a more general case, namely, we do not demand that the manifold is compact or the fundamental group is finitely generated. Among other things, we prove that the fundamental group of a forward complete and noncompact Finsler n-manifold (M,F) with nonnegative Ricci curvature and finite uniformity constant has polynomial growth of order ≤ n-1, and the first Betti number satisfies b₁(M) ≤ n-1. We also obtain some sufficient conditions to ensure that the fundamental group is finite or is trivial. Most of the results are new even for Riemannian manifolds.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-3-6,
author = {Bing Ye Wu},
title = {Some results on curvature and topology of Finsler manifolds},
journal = {Annales Polonici Mathematici},
volume = {107},
year = {2013},
pages = {309-320},
zbl = {1269.53040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-3-6}
}
Bing Ye Wu. Some results on curvature and topology of Finsler manifolds. Annales Polonici Mathematici, Tome 107 (2013) pp. 309-320. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-3-6/