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2017 | OriginalPaper | Chapter

Recent Results on Real Hypersurfaces in Complex Quadrics

Author : Young Jin Suh

Published in: Hermitian–Grassmannian Submanifolds

Publisher: Springer Singapore

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Abstract

In this survey article, first we introduce the classification of homogeneous hypersurfaces in some Hermitian symmetric spaces of rank 2. Second, by using the isometric Reeb flow, we give a complete classification for hypersurfaces M in complex two-plane Grassmannians \(G_2({\mathbb C}^{m+2})=SU_{2+m}/S(U_{2}U_{m})\), complex hyperbolic two-plane Grassmannians \(G_{2}^{*}({\mathbb C}^{m+2})=SU_{2,m}/S(U_{2}U_{m})\), complex quadric \(Q^m={ SO}_{m+2}/SO_{m}SO_{2}\) and its dual \(Q^{m *}= SO_{m,2}^{o}/SO_{m}SO_{2}\). As a third, we introduce the classifications of contact hypersurfaces with constant mean curvature in the complex quadric \(Q^m\) and its noncompact dual \(Q^{m *}\) for \(m \ge 3\). Finally we want to mention some classifications of real hypersurfaces in the complex quadrics \(Q^m\) with Ricci parallel, harmonic curvature, parallel normal Jacobi, pseudo-Einstein, pseudo-anti commuting Ricci tensor and Ricci soliton etc.

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Title: Recent Results on Real Hypersurfaces in Complex Quadrics
Author: Young Jin Suh
Publisher: Springer Singapore
Book: Hermitian–Grassmannian Submanifolds
Print ISBN: 978-981-10-5555-3

Electronic ISBN: 978-981-10-5556-0

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-981-10-5556-0_28

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