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Homogeneous quaternionic Kaehler structures and quaternionic hyperbolic space

M. Castrillon Lopez·P. M. Gadea·A. F. Swann
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Abstract

An explicit classification of homogeneous quaternionic Kaehler structures by real tensors is derived and we relate this to the representation-theoretic description found by Fino. We then show how the quaternionic hyperbolic space HH(n) is characterised by admitting homogeneous structures of a particularly simple type. In the process we study the properties of different homogeneous models for HH(n).

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M. Castrillon Lopez, P. M. Gadea, A. F. Swann. 2005-04-27. Homogeneous quaternionic Kaehler structures and quaternionic hyperbolic space. https://arxiv.org/abs/math/0504550

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