Hamiltonian-minimal Lagrangian submanifolds in complex space forms

Details Hamiltonian-minimal Lagrangian submanifolds in complex space forms Hamiltonian-minimal Lagrangian submanifolds in complex space forms

2004-12-02

arxiv.org/abs/math/0412046v1

Mathematics

Differential Geometry

28 pages

Scientific paper

Using Legendrian immersions and, in particular, Legendre curves in odd dimensional spheres and anti De Sitter spaces, we provide a method of construction of 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. In addition, new examples of minimal Lagrangian submanifolds in complex projective and hyperbolic spaces also appear. Making use of all of them, we get Hamiltonian-minimal and special Lagrangian cones in complex Euclidean space too.

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