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Some results on curvature and topology of Finsler manifolds

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Wu B.

Annales Polonici Mathematici

2013

tom 107

nr 3

309-320

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Wu B.

1 2013

Wyniki wyszukiwania

Some results on curvature and topology of Finsler manifolds