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On the b-completion of certain quotient spaces. (English) Zbl 0645.53036

Summary: Given a manifold M with a connection and a finite group A of affine transformations, we show that the b-completion (or Schmidt’s completion) of the quotient manifold M/A is the quotient, under the extended action of A, of the b-completion of M.

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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References:

[1] Bosshard, B., Commun. Math. Phys. 46, 263-268 (1976). · Zbl 0324.53023 · doi:10.1007/BF01609123
[2] Dodson, C. T. J. and Sulley, L. J., Lett. Math. Phys. 1, 301-307 (1977). · Zbl 0352.53023 · doi:10.1007/BF00398485
[3] Johnson, R. A., J. Math. Phys. 18, 898-902 (1977). · Zbl 0349.53052 · doi:10.1063/1.523357
[4] O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983, p. 188.
[5] Schmidt, B. G., Gen Rel. Grav. 1, 269-280 (1971). · Zbl 0332.53039 · doi:10.1007/BF00759538
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