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

Abstract: The warped product

N_{1} i m e s_{f} N_{2}

of two Riemannian manifolds

(N_{1}, g_{1})

and

(N_{2}, g_{2})

is the product manifold

N_{1} i m e s 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

i l d e M

is called a

C R

-warped product if it is a warped product

M_{T} i m e s_{f} N_{p} e r p

of a complex submanifold

M_{T}

and a totally real submanifold

M_{p} e r p

of

i l d e M

. In this article we survey recent results on warped product and

C R

-warped product submanifolds in Kaehler manifolds. Several closely related results will also be presented.

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