Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-20T01:39:04.074Z Has data issue: false hasContentIssue false
  • English
  • Français

Pencils Of Polarities In Projective Space

Published online by Cambridge University Press:  20 November 2018

Seymour Schuster
Seymour Schuster*
Affiliation:
Polytechnic Institute of Brooklyn
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.

1. Introduction. A polarity in complex projective space of two dimensions (S2) is completely determined by a self-polar triangle ABC, and a pair of corresponding elements: a point P and its polar line p. We denote the polarity by (ABC) (Pp). We follow Coxeter (2) in denning a pencil of polarities as the ∞1 polarities (ABC) (Pp) where A, B, C, P are fixed while p varies in a pencil of lines.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 119 - 144
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Baldus, R., Zur Klassification der ebenen und räumlichen Kollineationen, Sitz. Bayerischen Akad., 1928, 375–395.Google Scholar
2. Coxeter, H. S. M., The real projective plane (New York, 1949; Cambridge University Press, 1955).Google Scholar
3. Coxeter, H. S. M., Projective geometry, Math. Magazine, 23 (1949), 79–97.Google Scholar
4. Dempster, A. P. and Schuster, S., Constructions for poles and polars, Pacific J. Math., 5 (1955), 197–199.Google Scholar
5. Godeaux, L. and Rozet, O., Leçons de géométrie projective (2nd ed., Liège, 1952).Google Scholar
6. Hodge, W. V. D. and Pedoe, D., Methods of algebraic geometry, vol. 2 (Cambridge, 1952).Google Scholar
7. Reye, Th., Ueber Polfönfecke und Polsechsecke raumlicher Polarsysteme, J. reine angew. Math., 77 (1874), 269–288.Google Scholar
8. Sommerville, D. M. Y., An introduction to the geometry of n dimensions (London, 1929).Google Scholar
9. Todd, J. A., Projective and analytical geometry (London, 1947).Google Scholar
10. Veblen, O. and Young, J. W., Projective geometry, vol. 1 (Boston, 1910).Google Scholar
11. von Staudt, G. K. C., Geometrie der Lage (Nuremberg, 1847).Google Scholar