Abstract
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.
Highlights
The theory of degenerate submanifolds of semi-Riemannian manifolds is one of important topics of differential geometry
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 antiinvariant lightlike hypersurfaces
Summary
The theory of degenerate submanifolds of semi-Riemannian manifolds is one of important topics of differential geometry. In 5 , Kılıcand Sahin introduced radical anti-invariant lightlike submanifolds of a semi-Riemannian product manifold and gave some examples and results for lightlike submanifolds. The properties of Riemannian manifolds with semisymmetric symmetric and nonmetric connection have been studied by many authors 9–14. In 15 , Yasar et al have studied lightlike hypersurfaces in semi-Riemannian manifolds with semisymmetric nonmetric connection. We study lightlike hypersurfaces of a semi-Riemannian product manifold. We compute the Riemannian curvature tensor with respect to the quarter-symmetric nonmetric connection and give some results
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