On some Moment Maps and Induced Hopf Bundles in the Quaternionic Projective Space
Differential Geometry
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0001066,
title = {On some Moment Maps and Induced Hopf Bundles in the Quaternionic Projective Space},
author = {Liviu Ornea and Paolo Piccinni},
journal= {arXiv preprint arXiv:math/0001066},
year = {2007}
}
Comments
Revised version, a more complete proof of a statement and some references were added. LaTex, 21 pages, to be published in Int. J. Math