and, in particular, Legendre curves in odddimensional 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.
We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane C 2 by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves, respectively. Among this family, we characterize minimal, constant mean curvature, Hamiltonianminimal and Willmore surfaces in terms of simple properties of the curvature of the generating curves. As applications, we provide explicitly conformal parametrizations of known and new examples of minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in C 2 .
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