We will analyse systematically specific properties of Lorentzian manifolds,
paying a special attention to several variational problems applicable to
Mathematical Relativity and other areas of Theoretical Physics. Some techniques
can be extended to geometries which do not have an indefinite character, as the
classical Riemannian and Finslerian ones.

This project is based on the research developed in previous projects
by a stable base of the applicant team, which is now grouped in two sub-projects.