On the Hamiltonian minimality of normal bundles

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Abstract

A Hamiltonian minimal (shortly, H-minimal) Lagrangian submanifold in a Kähler manifold is a critical point of the volume functional under all compactly supported Hamiltonian deformations.We show that any normal bundle of a principal orbit of the adjoint representation of a compact simple Lie group G in the Lie algebra g of G is an H-minimal Lagrangian submanifold in the tangent bundle T g which is naturally regarded as Cm. Moreover, we specify these orbits with this property in the class of full irreducible isoparametric submanifolds in the Euclidean space.

Original languageEnglish
Title of host publicationReal and Complex Submanifolds
EditorsHyunjin Lee, Jürgen Berndt, Yoshihiro Ohnita, Byung Hak Kim, Young Jin Suh
PublisherSpringer New York LLC
Pages485-496
Number of pages12
ISBN (Electronic)9784431552147
DOIs
Publication statusPublished - 2014
EventSatellite Conference on Real and Complex Submanifolds ICM 2014 with 18th International Workshop on Differential Geometry - Daejeon, Korea, Republic of
Duration: 10 Aug 201412 Aug 2014

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume106
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceSatellite Conference on Real and Complex Submanifolds ICM 2014 with 18th International Workshop on Differential Geometry
Country/TerritoryKorea, Republic of
CityDaejeon
Period10/08/1412/08/14

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