Non-linear Morse-Bott functions on quaternionic Stiefel manifolds

Abstract In the Stiefel manifold X n , k , we replace Frankel linear height function by a quadratic one. We prove this is still a Morse–Bott function, whose structure of critical levels presents a dichotomy according to the sign of n − 2 k . The critical submanifolds are no longer Grassmannians but total spaces of fibrations of basis a product of two Grassmannians. We explicitly integrate the gradient flow.