Journal of Applied Mathematics
Volume 2012 (2012), Article ID 636782, 18 pages
http://dx.doi.org/10.1155/2012/636782
Research Article

Lightlike Submanifolds of a Semi-Riemannian Manifold of Quasi-Constant Curvature

D. H. Jin1 and J. W. Lee2

1Department of Mathematics, Dongguk University, Kyongju 780-714, Republic of Korea
2Department of Mathematics, Sogang University, Sinsu-dong, Mapo-gu, Seoul 121-742, Republic of Korea

Received 19 January 2012; Revised 29 February 2012; Accepted 14 March 2012

Academic Editor: Chein-Shan Liu

Copyright © 2012 D. H. Jin and J. W. Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the geometry of lightlike submanifolds ( 𝑀 , 𝑔 , 𝑆 ( 𝑇 𝑀 ) , 𝑆 ( 𝑇 𝑀 ⟂ ) ) of a semi-Riemannian manifold ( 𝑀 , ̃ 𝑔 ) of quasiconstant curvature subject to the following conditions: (1) the curvature vector field ζ of 𝑀 is tangent to 𝑀 , (2) the screen distribution 𝑆 ( 𝑇 𝑀 ) of 𝑀 is totally geodesic in 𝑀 , and (3) the coscreen distribution 𝑆 ( 𝑇 𝑀 ⟂ ) of 𝑀 is a conformal Killing distribution.