Preprint 38/2009

On Lightlike Geometry in Indefinite Kenmotsu Manifolds

Fortuné Massamba

Contact the author: Please use for correspondence this email.
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
MSC-Numbers: 53C15, 53C25, 53C50
Keywords and phrases: Lightlike hypersurfaces, Screen distribution, Indefinite Kenmostu space form
Download full preprint: PDF (216 kB)

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.

05.11.2022, 02:15