Geometry of warped product and CR-warped product submanifolds in Kaehler manifolds: modified version

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.

25 pages. arXiv admin note: substantial text overlap with arXiv:1307.0236