English

Non-linear Morse-Bott functions on quaternionic Stiefel manifolds

Differential Geometry 2021-01-11 v1

Abstract

In the Stiefel manifold Xn,kX_{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 n2kn-2k. 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.

Keywords

Cite

@article{arxiv.2004.05454,
  title  = {Non-linear Morse-Bott functions on quaternionic Stiefel manifolds},
  author = {Enrique Macías-Virgós and María José Pereira-Sáez and Daniel Tanré},
  journal= {arXiv preprint arXiv:2004.05454},
  year   = {2021}
}
R2 v1 2026-06-23T14:48:08.388Z