Abstract
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.
Acknowledgement
We are grateful to Professor Shoshichi Kobayashi for the stimulating discussion on the Riemannian aspects of the problem via e-mail.
Citation
Rezső L. Lovas. József Szilasi. "Homotheties of Finsler manifolds∗." SUT J. Math. 46 (1) 23 - 34, January 2010. https://doi.org/10.55937/sut/1280431135
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