Geodesics on product Lorentzian manifolds (Q1905012)

Let \({\mathcal M}\) be a product Lorentzian manifold \({\mathcal M}_0\times R\) where \({\mathcal M}_0\) is a complete Riemannian manifold and the Lorentzian metric of \({\mathcal M}\) depends on the time variable and has mixed terms. Using global variational methods, the authors prove existence and various properties of timelike and spacelike geodesics joining two given events of \({\mathcal M}\).