On Lightlike Geometry in Indefinite Kenmotsu Manifolds

Fortuné Massamba

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Submission date: 21. Jul. 2009 (revised version: July 2009)
Pages: 27
published in: Mathematica Slovaca, 62 (2012) 2, p. 315-344 
DOI number (of the published article): 10.2478/s12175-012-0012-2
Bibtex
MSC-Numbers: 53C15, 53C25, 53C50
Keywords and phrases: Lightlike hypersurfaces, Screen distribution, Indefinite Kenmostu space form
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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.