A basic inequality and new characterization of Whitney spheres in a complex space form
type: Item
instance of: scholarly article
title: A basic inequality and new characterization of Whitney spheres in a complex space form
zbMATH Open document ID: 1076.53072
DOI: 10.1007/BF02773534
author: Haizhong Li
author: Luc Vrancken
published in: Israel Journal of Mathematics
publication date: 2005-06-09T00:00:00Z
review text: The authors consider an \(n\)-dimensional Lagrangian submanifold \(M\) of the \(n\)-dimensional complex space form of constant holomorphic sectional curvature. The authors derive an inequality involving \(| \overline{\nabla} h| ^2,\) where \(h\) is the second fundamental form, and \(| \nabla^\perp \vec{H}| ^2,\) where \(\vec{H}\) is the mean curvature vector, that is \[ | \overline{\nabla} h| ^2\geqslant \frac{3n^2}{n +2}| \nabla^\perp \vec{H}| ^2 \] They classify all submanifolds that realize at every point the equality, giving a a characterization of the Whitney spheres in a complex space form.
reviewed by: Ricardo Sa Earp
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 2174710
zbMATH Keywords: Mean curvature
zbMATH Keywords: Lagrangian submanifold
zbMATH Keywords: Whitney sphere
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02773534
OpenAlex ID: W2142255475
Wikidata QID: Q125989816
description: scientific article; zbMATH DE number 2174710