Lorentzian compact manifolds: isometries and geodesics

Abstract

In this work we investigate families of compact Lorentzian manifolds in dimension four. We show that every lightlike geodesic on such spaces is periodic, while there are closed and non-closed spacelike and timelike geodesics. Their isometry groups are computed. We also show that there is a non trivial action by isometries of $\Heis_3(\RR)$ on the nilmanifold $S^1\times (Γ_k \bsh \Heis_3(\RR))$ for ${\Gamma }_k$ a lattice of $\Heis_3(\RR)$.

17 pages

References in corpus (2)

• Closed Geodesics in Lorentzian Surfaces
• Naturally reductive pseudo-Riemannian Lie groups in low dimensions