Minimal Legendrian submanifolds of \(S^{2n+1}\) and absolutely area-minimizing cones
type: Item
instance of: scholarly article
title: Minimal Legendrian submanifolds of \(S^{2n+1}\) and absolutely area-minimizing cones
zbMATH Open document ID: 1066.53108
author: Vincent Borrelli
author: Claudio Gorodski
published in: Differential Geometry and its Applications
publication date: 2004-11-19T00:00:00Z
review text: This paper gives a new and unified construction of compact homogeneous minimal Legendrian submanifolds of odd-dimensional spheres. It is shown that the cones over these submanifolds are absolutely area-minimizing. The construction is based on work of \textit{R. Harvey} and \textit{H. B. Lawson} in [Acta Math. 148, 47--157 (1982; Zbl 0584.53021)]. One family of these examples is constructed from isoparametric hypersurfaces in spheres. Another family uses orbits of isotropy representations of Hermitian symmetric spaces. Furthermore, it is shown that any Legendrian immersion of the 2-torus into the 5-sphere is regularly homotopic through Legendrian immersions to a minimal Legendrian embedding if and only if its Maslov class vanishes.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53D12
zbMATH DE Number: 2116891
zbMATH Keywords: Legendrian submanifold
zbMATH Keywords: Minimal immersion
zbMATH Keywords: Special Lagrangian cone
zbMATH Keywords: Maslov class
zbMATH Keywords: Hermitian symmetric space
zbMATH Keywords: Austere submanifolds
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: j.difgeo.2004.05.007
OpenAlex ID: W2077592913
Wikidata QID: Q115358015
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DOI: 10.1016/J.DIFGEO.2004.05.007
description: scientific article; zbMATH DE number 2116891