Molino, Pierre 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 Sémin. Gaston Darboux Géom. Topologie Différ. 1987-1988, 11-25 (1988). 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 Cited in 1 Document 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 Keywords:Riemannian foliations; transverse symplectic forms; structure Lie algebra PDFBibTeX XMLCite \textit{P. Molino}, Sémin. Gaston Darboux Géom. Topologie Différ. 1987--1988, 11--25 (1988; Zbl 0668.57023)