#### 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