(2) In the Lorentzian case, causality theory is a specific tool fully adapted to its particularities.
So, other sophisticated theories which may work in the Riemannian case, must be …

The aim of this paper is to study the geodesic connectedness of a complete static Lorentzian
manifold (M.<·,·> L) such that. if K is its irrotational timelike Killing vector field, the growth of …

We prove a variational principle for geodesics on a semi-Riemannian manifold M of arbitrary
index k and possessing k linearly independent Killing vector fields that generate a timelike …

In this paper we prove a multiplicity result for critical points of an indefinite functional on a
manifold by using a generalization of the Ljusternik–Schnirelman category. The abstract …

We study some global geometric properties of a static Lorentzian manifold Λ embedded in a
differentiable manifold M, with possibly non-smooth boundary∂ Λ. We prove a variational …

We prove a variational principle for geodesics on a semi-Riemannian manifold M of arbitrary
index k and possessing k linearly independent Killing vector fields that generate a timelike …

We study some global geometric properties of a static Lorentzian manifold A embedded in a
differentiable manifold M, with possibly non smooth boundary 8A. We prove a variational …

This is the textbook for a short course given by the authors during the 23rd Brazilian
Colloquium of Mathematics, held at the Instituto de Matemática Pura e Aplicada (IMPA), Rio …