Non-linear Morse-Bott functions on quaternionic Stiefel manifolds
Differential Geometry
2021-01-11 v1
Abstract
In the Stiefel manifold , 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 . 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}
}