Physical space-time and nonrealizable cr-structures

Abstract

Space-time views leading up to Einstein’s general relativity are described in relation to some of Poincaré’s early ideas on the subject. The basic geometry of twistor theory is introduced as it arises both from Minkowski space-time and the more general curved Einstein models. It is shown how this provides a CR-structure (this being, in essence, another of Poincaré’s pioneering concepts) in a natural way. Nonrealizable CR-structures can arise, and an example is presented, due to C. D. Hill, G. A. J. Sparling and the author, of a complex manifold-with-boundary which cannot be extended as a complex manifold beyond its C∞ boundary. © 1983 American Mathematical Society.