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Linear connections on light-like manifolds

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Koçak, Ş.
Limoncu, M.

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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.

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Scientific and Technological Research Council of Turkey (TUBITAK)

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Physics, Mathematics

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Turkish Journal of Mathematics

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