Results 1  10
of
11
Hamiltonianminimal lagrangian submanifolds in complex space forms
, 2004
"... 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 Hamiltonianminimal Lagrangian submanifolds in complex projective and hyperbolic spaces, including explicit one parameter famil ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
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 Hamiltonianminimal 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 Hamiltonianminimal and special Lagrangian cones in complex Euclidean space too.
CONSTRUCTION OF HAMILTONIANMINIMAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX EUCLIDEAN SPACE
, 2009
"... We describe several families of Lagrangian submanifolds in the complex Euclidean space which are Hminimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendri ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
(Show Context)
We describe several families of Lagrangian submanifolds in the complex Euclidean space which are Hminimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odddimensional unit sphere.
Hamiltonian stationary tori in Kähler manifolds
, 2008
"... A Hamiltonian stationary Lagrangian submanifold of a Kähler manifold is a Lagrangian submanifold whose volume is stationary under Hamiltonian variations. We find a sufficient condition on the curvature of a Kähler manifold of real dimension four to guarantee the existence of a family of small Hamilt ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
A Hamiltonian stationary Lagrangian submanifold of a Kähler manifold is a Lagrangian submanifold whose volume is stationary under Hamiltonian variations. We find a sufficient condition on the curvature of a Kähler manifold of real dimension four to guarantee the existence of a family of small Hamiltonian stationary Lagrangian tori.
ON HAMILTONIAN STATIONARY LAGRANGIAN SPHERES IN NONEINSTEIN KÄHLER SURFACES
, 706
"... Abstract. Hamiltonian stationary Lagrangian spheres in KählerEinstein surfaces are minimal. We prove that in the family of nonEinstein Kähler surfaces given by the product Σ1×Σ2 of two complete orientable Riemannian surfaces of different constant Gauss curvatures, there is only a (non minimal) Ham ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Hamiltonian stationary Lagrangian spheres in KählerEinstein surfaces are minimal. We prove that in the family of nonEinstein Kähler surfaces given by the product Σ1×Σ2 of two complete orientable Riemannian surfaces of different constant Gauss curvatures, there is only a (non minimal) Hamiltonian stationary Lagrangian sphere. This example is defined when the surfaces Σ1 and Σ2 are spheres. 1.
Spectral data for Hamiltonianminimal Lagrangian tori in CP 2
, 804
"... In this work, we find spectral data that allow to find Hamiltonianminimal Lagrangian tori in CP 2 in terms of theta functions of spectral curves. A Lagrangian submanifold in a Kähler manifold is called Hamiltonianminimal, ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
In this work, we find spectral data that allow to find Hamiltonianminimal Lagrangian tori in CP 2 in terms of theta functions of spectral curves. A Lagrangian submanifold in a Kähler manifold is called Hamiltonianminimal,
Equivariant gluing constructions of contact stationary . . .
 CALC. VAR. (2009) 35:57–102
, 2009
"... ..."
1 THE CLASSIFICATION OF HAMILTONIAN STATIONARY LAGRANGIAN TORI IN CP2 BY THEIR SPECTRAL DATA.
"... ar ..."
(Show Context)
HAMILTONIANMINIMAL SUBMANIFOLDS IN KAEHLER MANIFOLDS WITH SYMMETRIES
, 2004
"... Abstract. By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many nontrivial complete Hamiltonian minimal submanifolds in CP ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many nontrivial complete Hamiltonian minimal submanifolds in CP n and C n. 1.
CONSTRUCTION OF HAMILTONIANSTATIONARY LAGRANGIAN SUBMANIFOLDS OF CONSTANT CURVATURE ε IN COMPLEX SPACE FORMS M̃n(4ε)
"... ar ..."
If ξ1, ξ2 ∈ T[z]CP
"... The complex projective space CPn can be identified with the quotient manifold( ..."
Abstract
 Add to MetaCart
(Show Context)
The complex projective space CPn can be identified with the quotient manifold(