Cauchy R iemann - and Semi - invariant Warped product submanifolds

Abstract

In this research we consider the recent exploring problem of existence (or non existence) of warped product submanifold in known spaces, for this reason first we have discussed a necessary and sufficient condition in terms of two canonical structures on a Cauchy Riemannian CR-submanifold of a nearly käehler manifold under which the submanifold reduces to a locally CR-warped product manifold, More over an estimate for the second fundamental form is investigated. Also we have illustrated the proof of aninequality for squared norm of second fundamental form