Abstract:

In the paper we present new examples of Lagrangian submanifolds in the direct products $\mathbb{C} \mathbb{P}^n \times \mathbb{C} \mathbb{P}^n$, which are not the direct products
themselves. The construction method generalizes the notion of quaternion real structure and uses lagrangian embedding of the full flag variety $F^n$ into the direct product $\mathbb{C} \mathbb{P}^{n-1} \times ... \times \mathbb{C} \mathbb{P}^{n-1}$, where the number of projective space copies equals to $n$, found by D. Bykov.