On some Moment Maps and Induced Hopf Bundles in the Quaternionic Projective Space
Abstract
We describe a diagram containing the zero sets of the moment maps associated to the diagonal U(1) and Sp(1) actions on the quaternionic projective space HP^n. These sets are related both to focal sets of submanifolds and to Sasakian-Einstein structures on induced Hopf bundles. As an application, we construct a complex structure on the Stiefel manifolds V_2 (C^{n+1}) and V_4 (R^{n+1}), the one on the former manifold not being compatible with its known hypercomplex structure.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- January 2000
- DOI:
- 10.48550/arXiv.math/0001066
- arXiv:
- arXiv:math/0001066
- Bibcode:
- 2000math......1066O
- Keywords:
-
- Mathematics - Differential Geometry;
- 53C15;
- 53C25;
- 53C55
- E-Print:
- Revised version, a more complete proof of a statement and some references were added. LaTex, 21 pages, to be published in Int. J. Math