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arXiv · 0710.3031

On a rigidity condition for Berwald Spaces

Ricardo Gallego Torrome·Fernando Etayo
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Abstract

We show that which that for a Berwald structure, any Riemannian structure that is preserved by the Berwald connection leaves the indicatrix invariant under horizontal parallel transport. We also obtain the converse result: if $({\bf M},F)$ is a Finsler structure such that there exists a Riemannian structure that leaves invariant the indicatrix under parallel transport of the associated Levi-Civita connection, then the structure $({\bf M},F)$ is Berwald. As application, a necessary condition for pure Landsberg spaces is formulated. Using this criterion we provide an strategy to solve the existence or not of pure Landsberg surfaces

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Ricardo Gallego Torrome, Fernando Etayo. 2009-07-01. On a rigidity condition for Berwald Spaces. https://doi.org/10.5052/racsam.2010.07

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