Homotheties of Finsler manifolds

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 isomet...

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Bibliographic Details
Published inarXiv.org
Main Authors Lovas, R L, Szilasi, J
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.04.2009
Subjects
Vector spaces
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Summary: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.
ISSN:2331-8422