Geometry of warped product CR-submanifolds in Kaehler manifolds. II. (English) Zbl 0996.53045

Chen, Bang-Yen

Monatsh. Math. 134, No. 2, 103-119 (2001).

A \(CR\)-submanifold of a Kähler manifold is called a CR-warped product if it is given as a warped product of a holomorphic submanifold and a totally real submanifold. Let \(N_T\times_f N_\perp\) be a \(CR\)-warped product in \(\widetilde M\). Then the author proved in Part I [Monatsh. Math. 133, No. 3, 177-195 (2001; Zbl 0996.53044)] that the second fundamental form \(\sigma\) satisfies \(\|\sigma \|^2\geqq 2(\dim N_\perp)\|\nabla(\ln f)\|^2\) and he studies the equality case when \(\widetilde M=\mathbb C^n\). The purpose of this Part II is to study the equality case for \(\widetilde M=\mathbb CP^n\) and \(\widetilde M=\mathbb CH^n\).

Reviewer: K.Ogiue (Tokyo)

MSC:

53C55	Global differential geometry of Hermitian and Kählerian manifolds
32V30	Embeddings of CR manifolds
53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53B25	Local submanifolds
53C40	Global submanifolds

Keywords:

CR-submanifold; warped product; Kähler manifold

Citations:

Zbl 0996.53044