Three-dimensional Lie group actions on compact (4n+3)-dimensional geometric manifolds |
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Authors: | Yoshinobu Kamishima Tetsuro Udono |
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Affiliation: | a Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0397, Japan b Department of Mathematics, Kumamoto University, Kumamoto 860-8555, Japan |
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Abstract: | The (4n+3)-dimensional sphere S4n+3 can be viewed as the boundary of the quaternionic hyperbolic space and the group PSp(n+1,1) of quaternionic hyperbolic isometries extends to a real analytic transitive action on S4n+3. We call the pair (PSp(n+1,1),S4n+3) a spherical Q C-C geometry. A manifold M locally modelled on this geometry is said to be a spherical Q C-C manifold. We shall classify all pairs (G,M) where G is a three-dimensional connected Lie group which acts smoothly and almost freely on a compact spherical Q C-C manifold M, preserving the geometric structure. As an application, we shall determine all compact 3-pseudo-Sasakian manifolds admitting spherical Q C-C structures. |
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Keywords: | 53C55 57S25 |
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