General improved Chen's inequality for Warped product bi-slant submanifolds in Kenmotsu manifolds

Abstract

Recently, B.Y. Chen established a relationship for the squared norm of the second fundamental form (an extrinsic invariant) of warped product bi-slant submanifolds of Kenmotsu manifolds in terms of the warping function (an intrinsic invariant).  In this paper, we study warped product bi-slant submanfolds of Kenmotsu manifolds.  We obtain a sufficient necessary condition that a bi-slant submanifold is locally a warped product and prove a characterisation theorem for such submanifolds. Finally, we establish a general improved Chen type of inequality. The equality case is also investigated.