2014/08/11 by L. Kozma, Kozma, Laszlo, Takayoshi Ootsuka +1
Physics and Astronomy · #53B40 #53B50 #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1408.2322
openalex publication_date 2014/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a Finsler non-linear connection by a new simplified definition for not only regular case but also singular case. In regular case, it corresponds to non-linear connection part of Berwald's connection, but our connection is expressed not in line element space but in point-Finsler space. In this view we recognize Finsler metric L(x,dx) as a non-linear form, which is a natural generalisation of Riemannian metric having original expression, √gab(x)dxa dxb. Furthermore our formulae provide easier calculation rather than conventional treatments, so we think that they suits to application to physics. Our definition can be used in the singular case of Finsler metric, which correspond to gauged constraint systems in mechanics. Here we give some non trivial examples of constraint systems for exposition of validity of our connection.