Physical space-time and nonrealizable ${\text{CR}}$-structures
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In this article, the basic geometry of twistor theory is introduced as it arises both from Minkowski space-time and the more general curved Einstein models, and it is shown how this provides a CR-structure (this being, in essence, another of Poincare's poioneering concepts) in a natural way.Abstract:
Space-time views leading up to Einstein's general relativity are described in relation to some of Poincare'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 Poincare's poioneering concepts) in a natural way. Nonrealizable CR-structure 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/sup infinity/ boundary.read more
Citations
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On the pseudo-conformal geometry of hypersurfaces of the space of n complex variables
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Three-dimensional Cauchy?Riemann structures and second-order ordinary differential equations
Pawel Nurowski,George Sparling +1 more
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Twistor CR manifolds and three-dimensional conformal geometry
TL;DR: In this article, it was shown that a twistor CR manifold is locally imbeddable as a real hypersurface in C3 only if it is real-analytic with respect to a suitable atlas.
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Twistors in 2+1 dimensions
TL;DR: The geometry of twistors for (2+1)dimensional flat space-time is described in this paper, where functions on twistor space generate solutions of various field equations in spacetime.
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Robinson manifolds and Cauchy–Riemann spaces
TL;DR: The notion of a shear-free congruence of null geodesics (SNGs) in dimension 4 was introduced by Robinson as mentioned in this paper, who defined a Lorentz manifold (M, g) of dimension 2n? 4 with a bundle N?? TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N]? Sec N.
References
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