Symmetry in the geometry of metric contact pairs

We prove that the universal covering of a complete locally symmetric normal metric contact pair manifold with decomposable φ{symbol} is a Calabi-Eckmann manifold or the Riemannian product of a sphere and R. We show that a complete, simply connected, normal metric contact pair manifold with decomposable φ{symbol}, such that the foliation induced by the vertical subbundle is regular and reflections in the integral submanifolds of the vertical subbundle are isometries, is the product of globally φ{symbol}-symmetric spaces or the product of a globally φ{symbol}-symmetric space and R. Moreover in the first case the manifold fibers over a locally symmetric space endowed with a symplectic pair.