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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
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