On a Class of Geodesically Connected Lorentzian Manifolds

In this paper we study the geodesical connectedness of Lorentzian manifolds. We consider a connected manifold = 0× , where 0is a complete Riemannian manifold endowed with a Lorentzian metricgof splitting type. We prove that, under suitable hypotheses on the coefficients of the metricg,Mis geodesically connected.