2021/11/08 by S. Hajdú, Hajdu, S., Tom Mestdag +1
Mathematics · Physics and Astronomy · #53B40 #53C05 #53C30 #53C60 #Advanced Differential Geometry Research #Bundle #Combinatorics #Computer science #Connection (principal bundle) #Curvature #Differential Geometry (math.DG) #Euclidean space #FOS: Mathematics #FOS: Physical sciences #Fiber bundle #Finsler manifold #Generalization #Geometry #Homogeneous #Lie algebra #Lie group #Manifold (fluid mechanics) #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Nonlinear system #Physics #Pure mathematics #Ricci curvature #Space (punctuation)
paper · pdf · doi:10.48550/arxiv.2111.04411
openalex publication_date 2021/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
A nonlinear splitting on a fibre bundle is a generalization of an Ehresmann connection. An example is given by the homogeneous nonlinear splitting of a Finsler function on the total manifold of a fibre bundle. We show how homogeneous nonlinear splittings and nonlinear lifts can be used to construct submersions between Euclidean, Minkowski and Finsler spaces. As an application we consider a semisimple Lie algebra and use our methods to give new examples of Finsler functions on a reductive homogeneous space.