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MiS Preprint
38/2011
Screen conformal lightlike geometry in indefinite Kenmotsu space forms
Fortuné Massamba
Abstract
In this paper we deal with geometric aspects of lightlike hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field and whose shape operator is conformal to the shape operator of its screen distribution. We show that these hypersufaces are proper totally contact umbilical, semi-parallel and $\eta$-Einstein but not Ricci semi-symmetric. They are locally a product of lightlike curves and proper totally umbilical leaves of its screen distributions. Its mean curvature vectors have closed dual differential 1-forms. We also show that there exists an integrable distribution whose leave are space forms, proper totally umbilical, Einstein, locally symmetric and Ricci semi-symmetric. We finally characterize the relative nullity space in a screen conformal lightlike hypersurface of an indefinite Kenmotsu space form.
