Some results on curvature and topology of Finsler manifolds

• Autorzy: Bing Ye Wu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53B40: Finsler spaces and generalizations (areal metrics)
• 53C23: Global geometric and topological methods (\`a la Gromov); differential geometric analysis on metric spaces
• 58B20: Riemannian, Finsler and other geometric structures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2013
• Tom: 107
• Numer: 3
• Strony: 309-320

Daty

wydano

2013

Twórcy

autor

Bing Ye Wu

• Department of Mathematics, Minjiang University, Fuzhou, Fujiang 350108, China

Identyfikatory

DOI

10.4064/ap107-3-6