As we already pointed out the main difference between the point and orbit reduced spaces is the invariance properties of the submanifolds out of which they are constructed. More specifically, if we mimic in the optimal context the standard orbit reduction procedure, the optimal orbit reduced space that we should study is G · J−1(ρ)/G = J−1(O ρ )/G, where O ρ := G· ⊂ M/Aʹ G . The following pages constitute an in-depth study of this quotient and its relation with new (pre)-symplectic manifolds that can be used to reproduce the classical orbit reduction program and expressions.
Keywords
- Symplectic Form
- Symplectic Manifold
- Coadjoint Orbit
- Smooth Structure
- Homogeneous Manifold
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Optimal Orbit Reduction. In: Hamiltonian Reduction by Stages. Lecture Notes in Mathematics, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72470-4_14
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DOI: https://doi.org/10.1007/978-3-540-72470-4_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72469-8
Online ISBN: 978-3-540-72470-4
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