## 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