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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 178390, 17 pages
Research Article

Lightlike Hypersurfaces of a Semi-Riemannian Product Manifold and Quarter-Symmetric Nonmetric Connections

1Department of Mathematics, Faculty of Arts and Sciences, İnönü University, 44280 Malatya, Turkey
2Department of Mathematics, Faculty of Arts and Sciences, Hitit University, 19030 Çorum, Turkey

Received 28 March 2012; Revised 2 July 2012; Accepted 16 July 2012

Academic Editor: Jianya Liu

Copyright © 2012 Erol Kılıç and Oğuzhan Bahadır. 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.


We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical anti-invariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quarter-symmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.