On some Moment Maps and Induced Hopf Bundles in the Quaternionic Projective Space

Details On some Moment Maps and Induced Hopf Bundles in the Quaternionic Projective Space On some Moment Maps and Induced Hopf Bundles in the Quaternionic Projective Space

2000-01-12

arxiv.org/abs/math/0001066v2

Mathematics

Differential Geometry

Revised version, a more complete proof of a statement and some references were added. LaTex, 21 pages, to be published in Int.

Scientific paper

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.

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