Dualit\'e complexe entre sous-vari\'et\'es r\'eelles dans $\mathbb{P}^2(\mathbb{C})$

TL;DR

This paper introduces a new concept of semi-legendrian real submanifolds in complex 3-manifolds, establishes a unique lifting in $\

Contribution

It defines semi-legendrian submanifolds and demonstrates a complex duality between real submanifolds in projective space.

Findings

Real submanifolds of $\

Unique liftings to $\

Complex duality established

Abstract

We introduce a notion of semi-legendrian real submanifold in a complex manifold of dimension 3 and prove that real submanifolds of $\mathbb{C}^2$ can be uniquely lifted to $\mathbb{C}^3$. Then we deduce a complex duality between real submanifolds of $\mathbb{P}^2(\mathbb{C})$.