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MiS Preprint
38/2009
On Lightlike Geometry in Indefinite Kenmotsu Manifolds
Fortuné Massamba
Abstract
We investigate some geometric aspects of lightlike hypersurfaces of indefinite Kenmotsu manifolds, tangent to the structure vector field, by paying attention to the geometry of leaves of integrable distributions. Theorems on parallel vector fields, Killing distribution, geodesibility of those leaves are obtained. The geometrical configuration of such lightlike hypersurfaces and leaves of its screen integrable distributions are established. We show that any totally contact umbilical leaf of screen integrable distribution of a lightlike hypersurface cannot be an extrinsic sphere. We also prove the geometry any leaf of integrable distribution is closely related with the geometry of a normal bundle.