Geometry of Warped Product CR-Submanifolds in Kaehler Manifolds, II

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 2001Publisher:Springer Science and Business Media LLCJournal:Monatshefte f�r Mathematik, volume 134, pages 103-119 (issn: 0026-9255, eissn: 1436-5081,

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Authors: Chen, Bang-Yen;

doi: 10.1007/s006050170002 , 10.1007/s006050170019

Geometry of Warped Product CR-Submanifolds in Kaehler Manifolds, II

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Abstract

The author introduces a new class of CR-submanifolds in a Kähler manifold, which are called CR-warped products. Let \(M=N_T \times_f N_\perp\) be a CR-warped product in a Kähler manifold \(\widetilde M\), where \(N_T\) is a holomorphic submanifold and \(N_\perp\) is a totally real submanifold of \(\widetilde M\). Then, the author proves that the second fundamental form \(\sigma\) satisfies \(\|\sigma\|^2\geqq 2 \dim N_\perp\|\nabla(\ln f)\|^2\). He also investigates the case where the equality holds.

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Michigan State University
United States

Keywords

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Local submanifolds, Embeddings of CR manifolds, CR-submanifold, Global submanifolds, Global differential geometry of Hermitian and Kählerian manifolds, warped product, Kähler manifold

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