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

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 $\mathbb{P}^2(\mathbb{C})$.