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Projective collineations in a space of k-spreads

Published online by Cambridge University Press:  24 October 2008

R. S. Clark
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Extract

A collineation in a space of paths is defined as a point transformation which carries paths into paths. Such transformations were first studied by L. P. Eisenhart and M. S. Knebelman. Subsequently J. Douglas introduced the geometry of K-spreads and E. T. Davies has shown that the results for an affine space of paths can be extended to these more general spaces and written in a very elegant form by the aid of Lie derivation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 41 , Issue 3 , November 1945 , pp. 210 - 223
Copyright
Copyright © Cambridge Philosophical Society 1945

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References

I.Eisenhart, L. P. and Knebelmam, M. S.Displacements in a geometry of paths which carry paths into paths. Proc. Nat. Acad. Sci., Washington, 13 (1927), 38–42.CrossRefGoogle Scholar
II.Knebelman, M. S.Groups of collineations in a space of paths. Proc. Nat. Acad. Sci., Washington, 13. (1927), 396–400.CrossRefGoogle Scholar
III.Eisenhart, L. P.Non-Riemannian Geometry. Colloquium Publ. Amer. Math. Soc. 8 (1927).CrossRefGoogle Scholar
IV.Knebelmany, M. S.Collineations and motions in generalized spaces. Amer. J. Math. 51 (1929), 527–564.CrossRefGoogle Scholar
V.Douglas, J.Systems of K-dimensional manifolds in an N-dimensional space. Math. Ann. 105 (1931), 707–733.CrossRefGoogle Scholar
VI.Slebodzinski, W.Sur les transformations isomorphiques d'une variété a connexion affine. Math.-phys. Abh. Warschau, 39 (1932), 55–62.Google Scholar
VII.Eisenhart, L. P.Continuous Groups of Transformations. Princeton (1933).Google Scholar
VIII.Davies, E. T.On the isomorphic transformations of a space of K-spreads. J. London Math. Soc. (2), 18 (1943), 100–107.CrossRefGoogle Scholar
IX.Davies, E. T. Groups of motions in a metric space based on the notion of area. In course of publication in the Quart. J. Math. (Oxford).Google Scholar