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Réduction symplectique et feuilletages riemanniens; moment structural et théorème de convexité. (Symplectic reduction and Riemannian foliations; structural moment and the theorem of convexity). (French) Zbl 0668.57023

Riemannian foliations admitting transverse symplectic forms are considered. If \({\mathcal F}\) is such a foliation on a compact simply connected manifold V, then there exists a map J: \(V\to R^ p\) constant along the leaves. \(P=J(V)\) is a closed convex polyhedron. Here, p is the dimension of the structure Lie algebra of \({\mathcal F}\). Moreover, \(J^{- 1}(\partial P)\) is the union of singular closure of leaves of \({\mathcal F}\).
Reviewer: P.Walczak

MSC:

57R30 Foliations in differential topology; geometric theory
53C12 Foliations (differential geometric aspects)
58H99 Pseudogroups, differentiable groupoids and general structures on manifolds
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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