Screen conformal lightlike geometry in indefinite Kenmotsu space forms

Fortuné Massamba

Contact the author: Please use for correspondence this email.
Submission date: 07. Jul. 2011
Pages: 32
published in: International Electronic Journal of Geometry, 5 (2012) 2, p. 36-58 
Bibtex
with the following different title: Screen almost conformal lightlike geometry in indefinite Kenmotsu space forms
MSC-Numbers: 53C15, 53C25, 53C50
Keywords and phrases: Indefinite Kenmostu space form, Lightlike hypersurface, Relative nullity foliation
Download full preprint: PDF (203 kB)

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 η-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.