2007/01/31 by T. Dereli, Tekin Dereli, Şahin Koçak +6
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Combinatorics #Connection (principal bundle) #Differential Geometry (math.DG) #Existential quantification #FOS: Mathematics #Fundamental theorem of Riemannian geometry #Geometry #Manifold (fluid mechanics) #Mathematics #Metric connection #Pure mathematics #Topology (electrical circuits) #Torsion (gastropod) #math.DG
paper · pdf · doi:10.48550/arxiv.math/0701934
arxiv created 2007/01/31 · openalex publication_date 2007/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is well-known that a torsion-free linear connection on a light-like manifold (M,g) compatible with the degenerate metric g exists if and only if Rad(TM) is a Killing distribution. In case of existence, there is an infinitude of connections with none distinguished. We propose a method to single out connections with the help of a special set of 1-forms by the condition that the 1-forms become parallel with respect to this connection. Such sets of 1-forms could be regarded as an additional structure imposed upon the light-like manifold. We consider also connections with torsion and with non-metricity on light-like manifolds.