Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-29T00:38:15.113Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Measure of Sets of Parallel Linear Subspaces in Affine Space

Published online by Cambridge University Press:  20 November 2018

L. A. Santaló
L. A. Santaló*
Affiliation:
University of Buenos Aires
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let En be the n-dimensional euclidean real space and the group of unimodular affine transformations which operates on it. It is known that the sets of linear h-spaces Lh (0 < h < n) have no invariant measure with respect to u (5). We wish now to consider sets of elements

1.1

composed by q parallel subspaces of dimensions h1, h2, … , hq which transform transitively by .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 313 - 319
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Bonnesen, T. and Fenchel, W., Théorie der konvexen Kôrper, Ergebnisse der Mathematik (Berlin, 1934).Google Scholar
2. Cartan, E., La Théorie des groupes finis et continus et la géométrie difêrentielle traités par la méthode du repère mobile (Paris; Gauthier-Villars, 1937).Google Scholar
3. Chern, S. S., On integral geometry in Klein spaces, Ann. Math., 43 (1942), 178–189.Google Scholar
4. Kowalewski, G., Einfùhrung in die Determinantentheorie (New York: Chelsea Publ., 1948).Google Scholar
5. Santalo, L. A., Integral geometry in projective and affine spaces, Ann. Math., 51 (1950), 739–755.Google Scholar
6. Santalo, L. A., Sur la mesure des espaces linéaires qui coupent un corps convexe et problèmes qui s'y rattachent, Colloque sur les questions de réalité en Géométrie (Liège, 1955).Google Scholar
7. Santalo, L. A., Two applications of the integral geometry in affine and projective spaces, Publications Mathematicae Debrecen, 7 (1960), 226–237.Google Scholar