Bulletin of the
Korean Mathematical Society BKMS

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