Slant Lightlike Submanifolds of Semi-Riemannian Product Manifolds
DOI:
https://doi.org/10.5644/SJM.19.02.02Keywords:
Slant lightlike submanifold, totally umbilical lightlike submanifold, semi-Riemannian product manifoldAbstract
The aim of the present paper is to investigate geometric characteristics of slant lightlike submanifolds of semi-Riemannian product manifolds. We obtain characterization theorems for the existence of slant lightlike submanifolds of semi-Riemannian product manifolds. We also find a necessary and sufficient condition enabling the induced connection on slant lightlike submanifolds of semi-Riemannian product manifolds to be a metric connection. Then, we establish some results for the integrability of distributions associated with this class of lightlike submanifolds. Consequently, we investigate totally umbilical slant lightlike submanifolds of semi-Riemannian product manifolds. In particular, we prove that every totally umbilical slant lightlike submanifold of a semi-Riemannian product manifold is always totally geodesic.
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