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

Liviu Ornea·Paolo Piccinni
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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.

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Liviu Ornea, Paolo Piccinni. 2000-08-29. On some Moment Maps and Induced Hopf Bundles in the Quaternionic Projective Space. https://arxiv.org/abs/math/0001066

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