Vol. 227, No. 1, 2006

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Hamiltonian-minimal Lagrangian submanifolds in complex space forms

Ildefonso Castro, Haizhong Li and Francisco Urbano

Vol. 227 (2006), No. 1, 43–63
Abstract

Using Legendrian immersions and, in particular, Legendre curves in odd-dimensional spheres and anti-de Sitter spaces, we construct new examples of Hamiltonian-minimal Lagrangian submanifolds in complex projective and hyperbolic spaces, including explicit one-parameter families of embeddings of quotients of certain product manifolds. We also give new examples of minimal Lagrangian submanifolds in complex projective and hyperbolic spaces. Making use of all these constructions, we get Hamiltonian-minimal and special Lagrangian cones in complex Euclidean space as well.

Keywords
Hamiltonian-minimal, Lagrangian submanifolds, Legendrian immersions
Mathematical Subject Classification 2000
Primary: 53C42, 53B25
Secondary: 53A05, 53D12
Milestones
Received: 1 December 2004
Revised: 29 June 2005
Accepted: 13 July 2005
Published: 1 September 2006
Authors
Ildefonso Castro
Departamento de Matemáticas
Escuela Politécnica Superior
Universidad de Jaén
23071 Jaén
Spain
Haizhong Li
Department of Mathematical Sciences
Tsinghua University
100084 Beijing
P. R. China
Francisco Urbano
Departamento de Geometría y Topología
Universidad de Granada
18071 Granada
Spain