Relative nullity foliations and lightlike hypersurfaces in indeﬁnite Kenmotsu manifolds

This paper deals with the relative nullity distributions of lightlike hypersurfaces of indeﬁnite Kenmotsu space forms, tangent to the structure vector ﬁeld. Theorems on parallel vector ﬁelds are obtained. We give characterization theorems for the relative nullity distributions as well as for Einstein, totally contact umbilical and ﬂat lightlike hypersurfaces. We show that, under a certain condition, Einstein lightlike hypersurfaces in indeﬁnite Kenmotsu space forms have parallel screen distributions. We prove that on a parallel (or totally umbilical) lightlike hypersurface, the relative nullity space coincides with the tangent vector space.

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