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