We know the construction of Schubert cell complex structure for the case of Grassmann manifold $Gr_k(\mathbb{C}^n)$ i.e variety of all k- dimensional subspaces $V$ of $\mathbb{C}^n$.
Consider that there is bilinear form B on $\mathbb{C}^n$. How to give a Schubert cell structure on the set of all V, k- dimensional subspaces of $\mathbb{C}^n$ such that B restricted on V is nonsingular.
Thank you in advance. Any help will be appreciated.