On pseudo-umbilical surfaces with nonzero parallel mean curvature vector in \(\mathbb{C} P^m (\widetilde{c})\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 0989.53036
author: Noriaki Sato
publication date: 2002-08-01T00:00:00Z
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1610172
zbMATH Keywords: complex projective space
zbMATH Keywords: Fubini-Study metric
zbMATH Keywords: complete pseudo-umbilical surface
zbMATH Keywords: parallel mean curvature
zbMATH Keywords: extrinsic hypersphere
MaRDI profile type: Publication
title: On pseudo-umbilical surfaces with nonzero parallel mean curvature vector in \(\mathbb{C} P^m (\widetilde{c})\)
published in: Saitama Mathematical Journal
review text: Let \(\mathbb{C}\mathbb{P}^m(\widetilde c)\) be a complex \(m\)-dimensional complex projective space with the Fubini-Study metric of constant holomorphic curvature \(\widetilde c\). The author proves the following main theorem: NEWLINENEWLINENEWLINELet \(M\) be a complete pseudo-umbilical surface with nonzero parallel mean curvature vector in \(\mathbb{C}\mathbb{P}^m (\widetilde c)\). If \(M\) is isotropic and the second fundamental form of \(M\) is commutative, then \(M\) is an extrinsic hypersphere in a 3-dimensional real projective space \(\mathbb{R} \mathbb{P}^3 (\widetilde c/4)\) of \(\mathbb{C}\mathbb{P}^3 (\widetilde c)\).
reviewed by: V. T. Fomenko
description: scientific article; zbMATH DE number 1610172