Calibrations and Lagrangian submanifolds in the six sphere
type: Item
instance of: scholarly article
title: Calibrations and Lagrangian submanifolds in the six sphere
zbMATH Open document ID: 0952.53036
author: Bennett Palmer
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2000-01-27T00:00:00Z
review text: It is well-known that \(S^6\) carries a natural non-integrable almost complex structure with respect to which the standard metric is Hermitian (but not Kähler). The natural 2-form is non-degenerate but not closed. Unlike in the integrable Kähler case, \textit{N. Ejiri} [Proc. Am. Math. Soc. 83, 759-763 (1981; Zbl 0474.53051)] proved that any smooth Lagrangian submanifold in \(S^6\) is minimal with respect to the standard metric. Based on Ejiri's result, the paper under review studies variational properties of Lagrangian submanifolds and derives the second variational formula for them. The author then applies the formula to the case of certain natural Lagrangian submanifolds in \(S^6\) that are obtained from complex curves in \({\mathbb C} P^2\) through the Hopf fibration. The paper also describes the calibration property of the Lagrangian submanifolds.
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C38
zbMATH DE Number: 1230538
zbMATH Keywords: Ejiri's theorem
zbMATH Keywords: Lagrangian submanifold
zbMATH Keywords: Lagrangian Jacobi field
zbMATH Keywords: associative calibration
reviewed by: Yong-Geun Oh
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178224980
OpenAlex ID: W2079653259
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Wikidata QID: Q125621576
DOI: 10.2748/TMJ/1178224980
description: scientific article; zbMATH DE number 1230538