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Space time manifolds and contact structures. (English) Zbl 0715.53032
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.
Reviewer: D.Allison
53C15Differential geometric structures on manifolds
53C50Lorentz manifolds, manifolds with indefinite metrics
83C99General relativity