Morse-Bott functions from complex structures

We present a quadratic Morse-Bott function on the real Grassmannian of a symplectic vector space from a compatible linear complex structure. Its stable manifolds generalize the Lagrangian, symplectic, isotropic, and coisotropic Grassmannians to include the Grassmannians of linear subspaces that are neither isotropic, coisotropic, nor symplectic. The negative gradient flow deformation retracts these stable manifolds to compact homogeneous spaces for the unitary group.