Space time manifolds and contact structures
This paper is an attempt to relate the theory of contact manifolds of Lorentzian geometry, and ultimately, to general relativity. The definitions of an almost contact manifold, contact manifold, and regular contact manifold are extended to the case of a semi-Riemannian manifold. A contact spacetime is defined to be a contact manifold with a semi- Riemannian metric of Lorentzian signature. The author shows that any odd dimensional strongly causal spacetime carries a regular contact structure. The Gödel universe is shown to be an example of a non- regular contact spacetime. A brief discussion of contact CR submanifolds in the context of semi-Riemannian manifolds is given. The idea here is that a 4-dimensional spacetime might be a contact CR submanifold of an ambient (necessarily odd-dimensional) contact manifold. References 15-27 were omitted from publication.
scientific article; zbMATH DE number 4178049