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Minimal surfaces with low index in the three-dimensional sphere
In the present paper, the author gives a characterization of the Clifford torus among the minimal surfaces of the three-dimensional sphere in terms of its index.
Lagrangian submanifolds of $C^{n}$ with conformal Maslov form and the Whitney sphere
The Lagrangian submanifolds of the complex Euclidean space with conformal Maslov form can be considered as the Lagrangian version of the hypersurfaces of the Euclidean space with constant meanExpand
LAGRANGIAN SURFACES IN THE COMPLEX EUCLIDEAN PLANE WITH CONFORMAL MASLOV FORM
We completely classify the compact orientable Lagrangian surfaces in the complex Euclidean plane with conformal Maslov form, obtaining a new family of embedded Lagrangian tori. 1
HAMILTONIAN-MINIMAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX SPACE FORMS
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 inExpand
Twistor holomorphic Lagrangian surfaces in the complex projective and hyperbolic planes
We completely classify all the twistor holomorphic Lagrangian immersions in the complex projective plane ℂℙ2, i.e. those Lagrangian immersions such that their twistor lifts to the twistor space overExpand
Isotropic totally real submanifolds
A Willmore functional for compact surfaces of complex projective plane
where H denotes the mean curvature vector of the immersion φ, K the sectional curvature of M restricted to Σ and dA the canonical measure of the induced metric. This functional has been extensivelyExpand
New examples of minimal Lagrangian tori in the complex projective plane
A new family of minimal Lagrangian tori in the complex projective plane is constructed. This family is characterized by its invariability by a one-parameter group of holomorphic isometries of theExpand
Closed conformal vector fields and Lagrangian submanifolds in complex space forms
We study a wide family of Lagrangian submanifolds in non flat complex space forms that we will call pseudoumbilical because of their geometric properties. They are determined by admitting a closedExpand
Quaternion CR-submanifolds of quaternion manifolds
A quaternion manifold (or quaternion Kaehlerian manifold [10]) is defined as a Riemannian manifold whose holonomy group is a subgroup of Sp(l). Sp(m)=Sp(l)xSp(m)/{±1}. The quaternion projective spaceExpand
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