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# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Some results on curvature and topology of Finsler manifolds

### Tom 107 / 2013

Annales Polonici Mathematici 107 (2013), 309-320 MSC: Primary 53C23; Secondary 53B40, 58B20. DOI: 10.4064/ap107-3-6

#### Streszczenie

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 $\le n-1$, and the first Betti number satisfies $b_1(M)\le n-1$. 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.

#### Autorzy

• Bing Ye WuDepartment of Mathematics
Minjiang University
Fuzhou, Fujiang 350108, China
e-mail

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