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Non-linear Morse-Bott functions on quaternionic Stiefel manifolds
- Source :
- Indag. Math 31 (2020) n{\deg}6 968-983
- Publication Year :
- 2020
-
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 $n-2k$. 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.
- Subjects :
- Mathematics - Differential Geometry
58E05 (Primary) 22E20, 22F30 (Secondary)
Subjects
Details
- Database :
- arXiv
- Journal :
- Indag. Math 31 (2020) n{\deg}6 968-983
- Publication Type :
- Report
- Accession number :
- edsarx.2004.05454
- Document Type :
- Working Paper