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Department of Mathematics, University of Kuwait

ABSTRACT

In this paper we find the G-structure of a pseudo-riemannian manifold (M,g) admitting a parallel partially null foliation F. Then we prove that this structure is in fact a reduction of the O-structure given by the metric, where O is the orthogonal group. As an example we give a complete description of the groups involved in the case of a Lorentz manifold with a parallel null 1-foliation.