Topology of complete Finsler manifolds with radial flag curvature bounded below

Abstract

We recently established a Toponogov type triangle comparison theorem for a certain class of Finsler manifolds whose radial flag curvatures are bounded below by that of a von Mangoldt surface of revolution (arXiv:1205.3913). In this article, as its applications, we prove the finiteness of topological type and a diffeomorphism theorem to Euclidean spaces.

arXiv commentThe version 2 was corrected as follows: we additionally assume G(ρ)\not= 0 in Theorems A and B, respectively. And some other minor changes have been done in the version 2. 12 pages, no figures. arXiv admin note: text overlap with arXiv:1205.3913

References in corpus (4)

• The cut locus and distance function from a closed subset of a Finsler manifold
• Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. I
• Grove-Shiohama type sphere theorem in Finsler geometry
• A Toponogov type triangle comparison theorem in Finsler geometry

Cited by in corpus (1)

• Grove-Shiohama type sphere theorem in Finsler geometry