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Axes of Points of Certain Linear Systems of Polarities

Published online by Cambridge University Press:  20 November 2018

Seymour Schuster
Seymour Schuster*
Affiliation:
University of Minnesota, Minneapolis, Minnesota
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In this issue honouring Professor Coxeter, I am pleased to present some results of an investigation that was prompted by questions which he himself raised over a decade ago.

With respect to a linear system of polarities in complex projective three-space, the polars of a fixed point Q form an axial pencil of planes. The axis of the pencil is called the axis of point Q with respect to the linear system of polarities. Since there are ∞3 axes and ∞4 lines in the space, not every line is an axis. The following discussion answers the questions of how many and which lines are axes with respect to the linear systems of polarities that have a fixed self-polar tetrahedron.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1072 - 1077
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Coxeter, H. S. M., The real projective plane, 2nd ed. (Cambridge, 1955).Google Scholar
2. Dempster, A. P. and Schuster, S., Constructions for poles and polars, Pacific J. Math., 5 (1955), 197–199.Google Scholar
Schuster, S., Pencils of polarities in projective space, Can. J. Math., 8 (1956), 119–144.Google Scholar