R. Kumar
University College of Engineering Punjabi University, Patiala
[ 1 ] - Non existence of totally contact umbilical slant lightlike submanifolds of indefinite Sasakian manifolds
We prove that there do not exist totally contact umbilical proper slant lightlike submanifolds of indefinite Sasakian manifolds other than totally contact geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally contact umbilical proper slant lightlike submanifolds of indefinite Sasakian space forms.
[ 2 ] - Ricci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds
We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.
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