Some results on curvature and topology of Finsler manifolds

Bing Ye Wu. "Some results on curvature and topology of Finsler manifolds." Annales Polonici Mathematici 107.3 (2013): 309-320. <http://eudml.org/doc/280855>.

@article{BingYeWu2013,
abstract = {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.},
author = {Bing Ye Wu},
journal = {Annales Polonici Mathematici},
keywords = {Finsler manifold; fundamental group; counting function; volume growth; polynomial growth; Ricci curvature},
language = {eng},
number = {3},
pages = {309-320},
title = {Some results on curvature and topology of Finsler manifolds},
url = {http://eudml.org/doc/280855},
volume = {107},
year = {2013},
}

TY - JOUR
AU - Bing Ye Wu
TI - Some results on curvature and topology of Finsler manifolds
JO - Annales Polonici Mathematici
PY - 2013
VL - 107
IS - 3
SP - 309
EP - 320
AB - 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.
LA - eng
KW - Finsler manifold; fundamental group; counting function; volume growth; polynomial growth; Ricci curvature
UR - http://eudml.org/doc/280855
ER -