A note on biharmonic submanifolds of product spaces
type: Item
instance of: scholarly article
title: A note on biharmonic submanifolds of product spaces
zbMATH Open document ID: 1285.53049
author: Julien Roth
published in: Journal of Geometry
publication date: 2013-10-30T00:00:00Z
review text: Biharmonic submanifolds of a Riemannian manifold are those for which the inclusion map is biharmonic. For submanifolds in a product of two space forms, the author describes biharmonicity by two geometric differential equations. They are equations for the mean curvature vector and involve operators derived from a natural involution \(F\) associated with the product structure. There are a few geometric corollaries under the assumption that \(FH\) is tangent to the submanifold, or at least not normal. All of them state that there are either no biharmonic submanifolds or they are strongly restricted, if \(FH\) is tangent and additional assumptions hold.
reviewed by: Andreas Gastel
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 6220945
zbMATH Keywords: biharmonic submanifolds
zbMATH Keywords: product spaces
MaRDI profile type: Publication
full work available at URL: s00022-013-0168-0
OpenAlex ID: W1983272449
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DOI: 10.1007/S00022-013-0168-0
description: scientific article; zbMATH DE number 6220945