A differentiable sphere theorem for compact Lagrangian submanifolds in complex Euclidean space and complex projective space

Isotropic Lagrangian Submanifolds in Complex Space Forms

In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.

Minimal Lagrangian Submanifolds in Complex Euclidean Space

Willmore Lagrangian Submanifolds in Complex Projective Space

Let M be an n -dimensional compact Willmore Lagrangian submanifold in a complex projective space CPn and let S and H be the squared norm of the second fundamental form and the mean curvature of M . Denote by ρ2 = S−nH2 the non-negative function on M , K and Q the functions which assign to each point of M the infimum of the sectional curvature and Ricci curvature at the point. We prove some inte...

isotropic lagrangian submanifolds in complex space forms

in this paper we study isotropic lagrangian submanifolds , in complex space forms . it is shown that they are either totally geodesic or minimal in the complex projective space , if . when , they are either totally geodesic or minimal in . we also give a classification of semi-parallel lagrangian h-umbilical submanifolds.

Construction of Hamiltonian-minimal Lagrangian Submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in the complex Euclidean space which are H-minimal, 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 odd-dimensional unit sphere.