Classification of real hypersurfaces in complex hyperbolic space in terms of constant \(\phi\)-holomorphic sectional curvatures
type: Item
instance of: scholarly article
zbMATH Open document ID: 1004.53015
author: Dong Joo Sohn
author: Young Jin Suh
publication date: 2002-04-08T00:00:00Z
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1725467
MaRDI profile type: Publication
title: Classification of real hypersurfaces in complex hyperbolic space in terms of constant \(\phi\)-holomorphic sectional curvatures
published in: Kyungpook Mathematical Journal
review text: If \(M\) is a real hypersurface of the complex hyperbolic space \(\mathbb{C} H^n\) (of constant holomorphic sectional curvature \(-4)\). An almost contact structure \((\varphi,\xi)\) is induced on it by the following conditions: \(J\xi\) is a unit normal of \(M\) and \(\varphi\) is the tensor field with kernel \(\mathbb{R}\xi\) satisfying \(\varphi X=JX\) for \(X\perp\xi\). By definition, \(M\) has constant \(\varphi\)-holomorphical sectional curvature \(H\in\mathbb{R}\), if for every unit vector \(v\in T_xM\) perpendicular to \(\xi_x\) the sectional curvature of \(\text{span} \{v,\varphi v\}\) equals \(H\). The authors derive a classification of these real hypersurfaces of constant \(\varphi\)-holomorphical sectional curvature. But the reviewer cannot see that the classification is complete, because he cannot reduce the problem to the cases (A) and (B) on the basis of the formulas (2.5) and (2.7) (see p. 805; notice that the numbers \(\overline \lambda_j\) are not complex conjugates of the \(\lambda_j)\).
reviewed by: Helmut Reckziegel
description: scientific article; zbMATH DE number 1725467