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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
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