A symplectic reduction for pseudo-Riemannian manifolds with compatible almost product structures, Beiträge Algebra Geom

Abstract. We consider a manifold M with a pseudo-Riemannian metric g and an almost product structure P such that g(P (X), P (Y)) = −g(X, Y). We suppose that the almost product structure P is parallel with respect to the Levi-Civita connection of g. These induce a natural symplectic structure onM. We consider an isometric action of a Lie group G on M preserving the pseudo-Riemannian metric and the almost product structure P. Then we prove a symplectic reduction theorem for such manifolds. We obtain a reduced manifold with a pseudo-Riemannian metric and a parallel almost product structure