Biharmonic hypersurfaces in \(E^5\) with zero scalar curvature
type: Item
instance of: scholarly article
title: Biharmonic hypersurfaces in \(E^5\) with zero scalar curvature
zbMATH Open document ID: 1333.53010
author: Deepika
author: Ram Shankar Gupta
published in: African Diaspora Journal of Mathematics
publication date: 2015-11-04T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.adjm/1439297863
review text: In 1991, \textit{B. Y. Chen} conjectured that all biharmonic submanifolds of Euclidean spaces are minimal [Soochow J. Math. 17, No. 2, 169--188 (1991; Zbl 0749.53037)]. While this conjecture in its general form is still open, substantial progress has been made under additional assumptions and in special cases. This article belongs to this direction of research. Using techniques of \textit{Th. Hasanis} and \textit{Th. Vlachos} [Math. Nachr. 172, 145--169 (1995; Zbl 0839.53007)], the authors prove that all biharmonic hypersurfaces of zero scalar curvature in Euclidean space \(E^5\) are minimal.
reviewed by: Hans-Peter Schröcker
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 6504476
zbMATH Keywords: biharmonic submanifold
zbMATH Keywords: scalar curvature
zbMATH Keywords: mean curvature vector
zbMATH Keywords: Chen's conjecture
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6504476