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On a rigidity condition for Berwald spaces

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

 Autoría: Torrome R.G., Etayo F.,

 Fuente: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 2010, 104, 69-80

 Editorial: Springer

 Año de publicación: 2010

 Nº de páginas: 12

 Tipo de publicación: Artículo de Revista

 DOI: 10.5052/RACSAM.2010.07

 ISSN: 1578-7303,1579-1505

 Proyecto español: MTM2008-01386

 Url de la publicación: https://doi.org/10.5052/RACSAM.2010.07

Autoría

RICARDO GALLEGO TORROME, RICARDO