CR-Warped Submanifolds in Kaehler Manifolds

Abstract

The warped product \(N_1\times _f N_2\) of two Riemannian manifolds \((N_1,g_1)\) and \((N_2,g_2)\) is the product manifold \(N_1\times N_2\) equipped with the warped product metric \(g=g_1+f^2 g_2\), where f is a positive function on \(N_1\). Warped products play very important roles in differential geometry as well as in physics. A submanifold M of a Kaehler manifold \(\tilde{M}\) is called a CR-warped product if it is a warped product \(M_T\times _f N_\perp \) of a complex submanifold \(M_T\) and a totally real submanifold \(M_\perp \) of \(\tilde{M}\). In this article we survey recent results on warped product and CR-warped product submanifolds in Kaehler manifolds. Several closely related results will also be presented.