Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T07:31:57.136Z Has data issue: false hasContentIssue false
  • English
  • Français

Projective collineations in a space of k-spreads

Published online by Cambridge University Press:  24 October 2008

R. S. Clark
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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