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Twisted local-product manifolds

Published online by Cambridge University Press:  20 January 2009

S. A. Robertson
S. A. Robertson
Affiliation:
Department of Pure Mathematics, The University, Liverpool, 3
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This note is concerned with “twisted“ analogues of the LP-structures (i.e.local-product structures) and grids of (4). To obtain these twisted structures, we modify the concepts of LP-structure and grid by removing the ordering of the local foliations involved in the definitions. The effect of this change is that global foliations need no longer exist, since the locally denned foils may now fit together to form self-intersecting immersed manifolds.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 1 , June 1970 , pp. 59 - 63
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

REFERENCES

(1) Charlap, L. S., Compact flat riemannian manifolds I, Ann. of Math. (2) 81 (1965), 15–30.CrossRefGoogle Scholar
(2) Charlap, L. S. and Vasquez, A. T., Compact flat riemannian manifolds II, Amer. J. Math 87 (1965), 551–563.CrossRefGoogle Scholar
(3) Hantzche, W. and Wendt, H., Dreidimensionale euklidische Raumformen, Math. Ann. 110 (1934–1935), 593–611.CrossRefGoogle Scholar
(4) Robertson, S. A., Grid manifolds, J. Differential Geometry (to appear).Google Scholar
(5) Wolf, J. A., Spaces of constant curvature (McGraw-Hill, New York, 1966).Google Scholar