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.
DERELİ, TEKİN; KOÇAK, ŞAHİN; and LİMONCU, MURAT (2008) "Linear Connections on Light-like Manifolds," Turkish Journal of Mathematics: Vol. 32: No. 1, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol32/iss1/5