Hamiltonian-minimal Lagrangian submanifolds in complex space forms

Ildefonso Castro, Haizhong Li and Francisco Urbano

Vol. 227 (2006), No. 1, 43–63

DOI: 10.2140/pjm.2006.227.43

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