ul 2 00 9 On a rigidity condition for Berwald Spaces July 1 , 2009

  • Ricardo Gallego Torrome
  • Published 2009

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 (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 (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.3 r.gallego.torrome@lancaster.ac.uk Partially supported during the writing of this note by EPRSC and Cockcroft Institute 2 etayof@unican.es. F.E is partially supported by Project MTM2008-01386/MTM (Spain).

Cite this paper

@inproceedings{Torrome2009ul20, title={ul 2 00 9 On a rigidity condition for Berwald Spaces July 1 , 2009}, author={Ricardo Gallego Torrome}, year={2009} }