Einstein \(H\)-umbilical submanifolds with parallel mean curvatures in complex space forms
type: Item
instance of: scholarly article
title: Einstein \(H\)-umbilical submanifolds with parallel mean curvatures in complex space forms
zbMATH Open document ID: 1055.53043
author: Setsuo Nagai
published in: Nihonkai Mathematical Journal
publication date: 2004-06-18T00:00:00Z
review text: The author classifies complete \(n\)-dimensional (\(n\geq 3\)) Einstein \(H\)-umbilical submanifolds with parallel mean curvature vector \(H\) in complex space forms \(\tilde{M}\) of (real) dimension \(2n\) and constant holomorphic curvature \(c\geq 0\). He shows that any such submanifold \(M\) is congruent either to a totally geodesic Lagrangian submanifold of \(\tilde{M}\) or to the product of a circle and the Euclidean space \(\mathbb{R}^{n-1}\).
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 2076006
zbMATH Keywords: space form
zbMATH Keywords: submanifold
zbMATH Keywords: mean curvature
zbMATH Keywords: umbilicity
reviewed by: Paweł Walczak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2076006