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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 140259, 11 pages
http://dx.doi.org/10.1155/2011/140259
Research Article

Characteristic Lightlike Submanifolds of an Indefinite 𝒮-Manifold

Department of Mathematics, Sogang University, Sinsu-Dong, Mapo-Gu, Seoul 121-742, Republic of Korea

Received 12 April 2011; Revised 12 August 2011; Accepted 23 August 2011

Academic Editor: Christian Corda

Copyright © 2011 Jae Won 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 characteristic 𝑟-lightlike submanifolds 𝑀 tangent to the characteristic vector fields in an indefinite metric 𝒮-manifold, and we also discuss the existence of characteristic lightlike submanifolds of an indefinite 𝒮-space form under suitable hypotheses: (1) 𝑀 is totally umbilical or (2) its screen distribution 𝑆(𝑇𝑀) is totally umbilical in 𝑀.