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

TL;DR

This paper proves a rigidity theorem for Lagrangian submanifolds in complex Euclidean and projective spaces that possess a conformal Maslov form, highlighting their geometric constraints.

Contribution

It introduces a new rigidity result specifically for Lagrangian submanifolds with conformal Maslov form in $C^n$ and $CP^n$, expanding understanding of their geometric properties.

Findings

Rigidity theorem established for Lagrangian submanifolds with conformal Maslov form.

Characterization of geometric constraints for such submanifolds.

Extension of known rigidity results to new classes of Lagrangian submanifolds.

Abstract

In this paper, we obtain a rigidity theorem for Lagrangian submanifolds of $C^n$ and $CP^n$ with conformal Maslov form.