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research article
The symplectic normal space of a cotangent-lifted action
Perlmutter, M.
•
Rodriguez-Olmos, M.
•
Sousa-Dias, M. E.
For the cotangent bundle T*Q of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal space at any point. We show that this space splits as the direct sum of the cotangent bundle of a linear space and a symplectic linear space coming from reduction of a coadjoint orbit. This characterization of the symplectic normal space can be expressed solely in terms of the group action on the base manifold and the coadjoint representation. Some relevant particular cases are explored. (C) 2007 Elsevier B.V. All rights reserved.
Type
research article
Web of Science ID
WOS:000256869000005
Authors
Perlmutter, M.
•
Rodriguez-Olmos, M.
•
Sousa-Dias, M. E.
Publication date
2008
Published in
Volume
26
Start page
277
End page
297
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
November 30, 2010
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