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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.13 no.3 Temuco oct. 2011

http://dx.doi.org/10.4067/S0719-06462011000300005 

CUBO A Mathematical Journal Vol.13, No'03, (69-89). October 2011

 

Lightlike Geometry of Leaves in Indefinite Kenmotsu Manifolds

 

Fortuné Massamba

Department of Mathematics, University of Botswana, Private Bag 0022 Gaborone, Botswana. email: massfort@yahoo.fr, massambaf@mopipi.ub.bw


ABSTRACT

In this paper, we study some aspects of the geometry of leaves of integrable distributions of lightlike hypersurfaces in indefinite Kenmotsu manifolds, tangent to the structure vector field. Theorems on parallel vector field, Killing distribution, geodesibility of lightlike hypersurfaces are obtained. Some characterization Theorems of leaves of integrable distributions are given. We prove that there exists a distribution, subset of the screen distribution, in which, under the integrability condition, any totally contact umbilical leaf is an extrinsic sphere.

Keywords: Lightlike hypersurface; Indefinite Kenmotsu manifold; Screen distribution.

Mathematics Subject Classification: 53C15, 53C25, 53C40, 53C50.


RESUMEN

En este trabajo se estudian algunos aspectos de la geometría de las hojas de distribuciones integrables de las hipersuperficies luminosas en variedades de Kenmotsu indefinidas, tangentes a la estructura de un campo vectorial. Se obtienen algunos teoremas sobre el campo de vectores paralelo, distribución de Killing y geodesbilidad de hipersuperficies liminosas. Se dan algunos teoremas de caracterización de las hojas de las distribuciones integrables. Se demuestra que existe una distribución, subconjunto de la distribución de la pantalla, en la que, bajo la condición de integrabilidad, cualquier contacto con la hoja umbilical es una esfera extrónseca.


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[15] F. Massamba, On Lightlike geometry in indefinite Kenmotsu manifolds, to appear in Mathe-matica Slovaca.         [ Links ]

[16] F. Massamba, On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds, J. Geom, 95 (2009), 73-89.         [ Links ]


Received: August 2009. Revised: August 2010.