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International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 545-553
http://dx.doi.org/10.1155/S0161171290000783

Space time manifolds and contact structures

Department of Mathematics and Statistics, University of Windsor, Ontario, Windsor N9B 3P4, Canada

Received 27 February 1989

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new class of contact manifolds (carring a global non-vanishing timelike vector field) is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic) spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.