Lightlike submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection
Bull. Korean Math. Soc. 2010 Vol. 47, No. 5, 1089-1103
https://doi.org/10.4134/BKMS.2010.47.5.1089
Published online September 1, 2010
Ahmet Y\{u}cesan and Erol Ya\c{s}ar
Department of Mathematics, Department of Mathematics
Abstract : In this paper, we study lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. We obtain a necessary and a sufficient condition for integrability of the screen distribution. Then we give the conditions under which the Ricci tensor of a lightlike submanifold with a semi-symmetric non-metric connection is symmetric. Finally, we show that the Ricci tensor of a lightlike submanifold of semi-Riemannian space form is not parallel with respect to the semi-symmetric non-metric connection.
Keywords : lightlike submanifolds, semi-symmetric non-metric connection, Levi-Civita connection, Ricci tensor
MSC numbers : 53B15, 53B30, 53C05, 53C50
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