Homotheties of Finsler manifolds

Details Homotheties of Finsler manifolds Homotheties of Finsler manifolds

2009-04-21

arxiv.org/abs/0904.3228v1

Mathematics

Differential Geometry

13 pages

Scientific paper

We give a new and complete proof of the following theorem, discovered by Detlef Laugwitz: (forward) complete and connected finite dimensional Finsler manifolds admitting a proper homothety are Minkowski vector spaces. More precisely, we show that under these hypotheses the Finsler manifold is isometric to the tangent Minkowski vector space of the fixed point of the homothety via the exponential map of the canonical spray of the Finsler manifold.

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