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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
Jul 21, 2009
Published:
Jul 21, 2009
MSC Codes:
53C15, 53C25, 53C50
Keywords:
Lightlike hypersurfaces, Screen distribution, Indefinite Kenmostu space form

Related publications

inJournal
2012 Journal Open Access
Fortuné Massamba

On lightlike geometry in indefinite Kenmotsu manifolds

In: Mathematica Slovaca, 62 (2012) 2, pp. 315-344