• Corpus ID: 115159514

Rigidity Theorems For Lagrangian Submanifolds of $C^n$ and $CP^n$ With Conformal Maslov Form

  title={Rigidity Theorems For Lagrangian Submanifolds of \$C^n\$ and \$CP^n\$ With Conformal Maslov Form},
  author={Xiaoli Chao and Yuxin Dong},
  journal={arXiv: Differential Geometry},
In this paper, we obtain a rigidity theorem for Lagrangian submanifolds of $C^n$ and $CP^n$ with conformal Maslov form. 



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 mean


The study of Lagrangian submanifolds in K¨ahler manifolds and in the nearly K¨ahler six-sphere has been a very active field over the last quarter of century. In this article we survey the main

Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length

Let \(\text M\)be an n-dimensional manifold which is minimally immersed in a unit sphere \(S^{n+p}\)of dimension \(n+p.\)

Lectures on Symplectic Manifolds

Introduction Symplectic manifolds and lagrangian submanifolds, examples Lagrangian splittings, real and complex polarizations, Kahler manifolds Reduction, the calculus of canonical relations,

Jacobi's elliptic functions and Lagrangian immersions

  • Bang-Yen Chen
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 1996
First, we establish a sharp inequality between the squared mean curvature and the scalar curvature for a Lagrangian submanifold in a nonflat complex-space-form. Then, by utilising the Jacobi's

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 closed

Pseudo holomorphic curves in symplectic manifolds

Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called

An intrinsic theorem for minimal submanifolds in a sphere

  • Archiv der Math .
  • 1985