IJPAM: Volume 11, No. 4 (2004)

CONFORMAL SCREEN ON LIGHTLIKE
HYPERSURFACES

C. Atindogbe$^1$, K.L. Duggal$^2$
$^1$Institut of Mathematical and Physical Sciences (IMSP)
P.O. Box 613, Porto-Novo, BENIN
$^2$Department of Mathematics
University of Windsor
Windsor, Ontario, N9B3P4, CANADA
e-mail: yq8@uwindsor.ca


Abstract.We study some properties of a lightlike hypersurface $M$, of a Lorentzian manifold, whose shape operator is conformal to the shape operator of its screen distribution. We prove that some specified aspects of the null geometry of $M$ reduce to the Riemannian geometry of a leaf of its screen distribution. As a physical relevance, we show that there exists such a class of screen globally conformal lightlike hypersurfaces of $4$-dimensional stationary non-flat spacetimes which admit a Killing horizon.

Received: January 9, 2004

AMS Subject Classification: 53C20, 53C50, 83C40

Key Words and Phrases: lightlike hypersurface, conformal screen, stationary spacetime

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 11
Issue: 4