Lorentzian isotropic Lagrangian immersions

Minimal Lagrangian isotropic immersions in indefinite complex space forms

Isometric immersions into Lorentzian products

We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed into one of the Lorentzian products Sn×R1 or Hn×R1. This condition is expressed in terms of its first and second fundamental forms, the tangent and normal projections of the vectical vector field. As applications, we give an equivalent condition in a spinorial way and we deduce the...

On isometric Lagrangian immersions

This article uses Cartan-Kähler theory to show that a small neighborhood of a point in any surface with a Riemannian metric possesses an isometric Lagrangian immersion into the complex plane (or by the same argument, into any Kähler surface). In fact, such immersions depend on two functions of a single variable. On the other hand, explicit examples are given of Riemannian three-manifolds which ...

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.