2007/10/31 by Ricardo Gallego Torromé, Ricardo Gallego Torrome, Fernando Etayo · 15 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Connection (principal bundle) #Converse #Geometry #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Parallel transport #Physics #Pure mathematics #Quantum mechanics #Rigidity (electromagnetism) #math.DG #msc:53C05 #msc:53C60
paper · pdf · doi:10.5052/racsam.2010.07
published in Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas 104(1), 69-80 (Springer Science+Business Media) · 19 pages; version acepted for publication in RACSAM
arxiv created 2009/07/01 · openalex publication_date 2010/03/01 · arxiv updated 2020/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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