Abstract
We introduce GCR-lightlike submanifolds of indefinite Cosymplectic manifolds and give an example. We also study the existence of this class in indefinite Cosymplectic space form. Then we prove that there does not exist a totally contact umbilical GCR-lightlike submanifold of an indefinite Cosymplectic manifold other than totally contact geodesic GCR-lightlike submanifold and moreover it is a totally geodesic GCR-lightlike submanifold.
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