Homogeneous Lagrangian foliations on complex space forms

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.

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.

Normal forms on contracting foliations: smoothness and homogeneous structure

In this paper we consider a diffeomorphism f of a compact manifold M which contracts an invariant foliation W with smooth leaves. If the differential of f on TW has narrow band spectrum, there exist coordinates Hx : Wx → TxW in which f |W has polynomial form. We present a modified approach that allows us to construct mapsHx that depend smoothly on x along the leaves of W . Moreover, we show tha...

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 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...

Minimal Lagrangian isotropic immersions in indefinite complex space forms