Contact Lorentzian manifolds
The paper under review contains an announcement of the classification of contact Lorentzian manifolds of constant sectional curvature in dimension \(>3\), as well as three-dimensional homogeneous contact Lorentzian manifolds. The proof is mainly based on the 1-1 correspondence between Riemannian contact structures -- see, e.g., \textit{D. E. Blair} [Riemannian geometry of contact and symplectic manifolds. Boston, MA: Birkhäuser (2002; Zbl 1011.53001)] -- and Lorentzian contact structures, described explicitly by the author in the paper. The paper also investigates properties of contact Lorentzian manifolds, by analogy with the Riemannian case. For instance, the author proves that a Sasakian contact Lorentzian manifold is K-contact, and proves the converse in the case of three-dimensional manifolds.
locally symmetric and homogeneous contact pseudo-metric three manifolds
scientific article; zbMATH DE number 5957568
scientific article