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Comersions and 1-connectedness

Published online by Cambridge University Press:  24 October 2008

F. J. Flaherty
F. J. Flaherty
Affiliation:
Oregon State University
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Abstract

A generalization of the notion of Riemannian submersion is given for submersions of a Lorentzian manifold onto a Riemannian manifold of one lower dimension. These maps are called comersions. A comersion induces a surjection of the space of causal curves in the domain manifold onto curves of bounded length in the image manifold. Thus if the source space is causally 1-connected, the target space is 1-connected.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 1 , January 1977 , pp. 143 - 147
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

(1)Flaherty, F.Lorentzian manifolds of non-positive curvature, II. Proc. Amer. Math. Soc. 48 (1975), 199–202.CrossRefGoogle Scholar
(2)Gray, A.Riemannian submersions, Technical Report University of Maryland, TR 69–130, (1969).Google Scholar
(3)Hawking, S. and Ellis, G.The large scale structure of space-time (Cambridge University Press, Cambridge 1973).CrossRefGoogle Scholar
(4)Hermann, R.A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle. Proc. Amer. Math. Soc. 11 (1960), 236–242.CrossRefGoogle Scholar
(5)Kobayashi, S.Riemannian manifolds without conjugate points. Ann. Mat. Pura Appl. 53 (1961), 149–155.CrossRefGoogle Scholar
(6)Kronheimer, E.Time-ordering and topology. J. Gen. Rel. and Gravitation 1 (1971), 261–268.CrossRefGoogle Scholar
(7)Milnor, J.Morse theory, Annals of Mathematics Studies No. 51 (Princeton University Press, Princeton, 1963).Google Scholar
(8)O'neill, B.The fundamental equations of a submersion. Michigan Math. J. 13 (1966), 459–469.CrossRefGoogle Scholar
(9)Uhlenbeck, K.A Morse theory for geodesies on a Lorentz manifold. Topology 14 (1975), 69–90.CrossRefGoogle Scholar
(10)Reinhart, B.Foliated manifolds with bundle-like metrics. Ann. of Math. 69 (1959), 119–132.CrossRefGoogle Scholar