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On bundle completion of parallelizable manifolds

Published online by Cambridge University Press:  24 October 2008

C. T. J. Dodson  and
L. J. Sulley
C. T. J. Dodson
Affiliation:
University of Lancaster
L. J. Sulley
Affiliation:
University of Lancaster
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Abstract

In (5), Schmidt devised a procedure for completing a space-time M by adjoining a boundary ∂M called the b-boundary. Bosshard(1) and Johnson(4) have shown that certain Friedmann and Schwarzschild space-times have non-Hausdorff b-completions.

In (2), (3), the first author considered a modification of the b-completion which gives a Hausdorff completion in the Friedmann case. The modification used a parallelization of the space-time and can be given in terms of the linear connexion determined by the parallelization. We show that the completion obtained is the Cauchy completion in a particular Riemannian metric on the manifold and so is always Hausdorff.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 3 , May 1980 , pp. 523 - 525
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

(1)Bosshard, B.On the b-boundary of the closed Friedmann model. Commun. Math. Phys. 46 (1976), 263–268.CrossRefGoogle Scholar
(2)Dodson, C. T. J.A new bundle completion for parallelizable space-times. Gen. Rel. Grav. (1979) (in press).CrossRefGoogle Scholar
(3)Dodson, C. T. J.Space-time edge geometry. Int. J. Th. Phys. 17, (1978), 389–504.Google Scholar
(4)Johnson, R. A.The bundle boundary in some special cases. J. Math. Phys. 18 (1977), 898–902.CrossRefGoogle Scholar
(5)Schmidt, B. G.A new definition of singular points in general relativity. Gen. Rel. Grav. 1, (1971), 269–280.CrossRefGoogle Scholar