IJPAM: Volume 46, No. 1 (2008)

SOME PROPERTIES OF LIGTHLIKE HYPERSURFACES
IN SEMI-REMANNIAN MANIFOLD

Erol Yasar$^1$, Ismet Ayhan$^2$
$^1$Ula Vocational High School
Mugla University
Ula, Mugla, TURKEY
email: yerol@mu.edu.tr
$^2$ Faculty of Education
Pamukkale University
Denizli, 20020, TURKEY
email: iayhan@pau.edu.tr


Abstract.In this paper, by using the method of Duggal and Bejancu, we study the geometry of a lightlike hypersurfaces of a semi-Riemannian manifold. First of all, we presented the theorems giving the conditions in which lightlike hypersurfaces are totally umbilical and flat. Moreover, we gave the theorems about symmetric case of Ricci tensor of reduced connection. Finally we obtain the corresponding theorems of the well-known theorems about hypersurfaces, like Euler and Meusnier Theorem, for lightlike hypersurfaces.

Received: February 10, 2008

AMS Subject Classification: 53B15, 53B30, 53C05, 53C50

Key Words and Phrases: lightlike hypersurface, totally umbilical, Levi-Civita connection, Ricci tensor

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 1