Minimal Lagrangian submanifolds in adjoint orbits and upper bounds on the first eigenvalue of the Laplacian.
type: Item
instance of: scholarly article
title: Minimal Lagrangian submanifolds in adjoint orbits and upper bounds on the first eigenvalue of the Laplacian.
zbMATH Open document ID: 1038.53073
author: Hajime Ono
published in: Journal of the Mathematical Society of Japan
publication date: 2003-06-30T00:00:00Z
review text: Let \(G\) be a compact semisimple Lie group, \(\mathcal G\) its Lie algebra, \((\;,\;)\) an \(\text{Ad}_G\)-invariant inner product on \(\mathcal G\) and \(M\) an adjoint orbit in \(\mathcal G\). In the paper under review the author takes in account the particular case when \((M,(\;,\;)_M)\) is a Kähler manifold with respect to its canonical complex structure, and \(L\) is a closed minimal Lagrangian submanifold of \(M\). In this picture he gives an upper bound of the first eigenvalue of the Laplacian on \(L\). The particular case when \(G=SU(n)\) is also nicely pointed out.
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1943309
zbMATH Keywords: minimal Lagrangian submanifold
zbMATH Keywords: Kählerian adjoint orbit
zbMATH Keywords: Laplacian
reviewed by: Mircea Puta
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1196890852
OpenAlex ID: W2095060311
DOI: 10.2969/JMSJ/1196890852
description: scientific article; zbMATH DE number 1943309