Linear connections on light-like manifolds

Dereli T., Kocak S., Limoncu M.

TURKISH JOURNAL OF MATHEMATICS, vol.32, no.1, pp.41-49, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 1
  • Publication Date: 2008
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.41-49
  • Anadolu University Affiliated: Yes

Abstract

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.