Strong rigidity of constant curvature Finsler manifolds

Details Strong rigidity of constant curvature Finsler manifolds Strong rigidity of constant curvature Finsler manifolds

2007-11-10

arxiv.org/abs/0711.1587v1

Mathematics

Differential Geometry

8 pages

Scientific paper

Here, an extension of the Obata-Tanno's theorem to Finsler geometry is
established and the following rigidity result is obtained; Every complete
connected Finsler manifold of positive constant flag curvature is isometrically
homeomorphic to an $n$-sphere equipped with a certain Finsler metric, and vise
versa.

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