A reduction scheme for phase spaces with almost Kähler symmetry: Regularity results for momentum level sets
✍ Scribed by Martin Otto
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 971 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0393-0440
No coin nor oath required. For personal study only.
✦ Synopsis
For phase spaces with a symmetry of an almost Köhler structure, extending the symplectic structure of phase space, a scheme of reduction 'is proposed, in which the decomposition into level sets of a momentum mapping is supplemented by a preliminary reduction with respect to orbit type under the action of the symmetry group. The joint process of reduction is shown to be applicable for all values of the momentum mapping and any orbit type considered, without meeting any of the usual obstructions encountered in reduction. Furthermore the proposed method gives rise to reduced phase spaces or Hamilton ian systems which cannot in general be obtained by the standard process, due to Marsden and Weinstein [8], [1], alone. Applicability is demonstrated for the cotangent bundle of Riemannian manifolds, which are shown to carry an almost Kahler structure extending the canonical symplectic structure. An almost Kàhler structure is constructed on the cotangent bundle for which the symmetries induced by isometries of the base manifold are almost KOhler automorphisms.