Geodesic
Axes of Points of Certain Linear Systems of Polarities
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 1072-1077

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Schuster, Seymour. Axes of Points of Certain Linear Systems of Polarities. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 1072-1077. doi: 10.4153/CJM-1967-097-1
@article{10_4153_CJM_1967_097_1,
     author = {Schuster, Seymour},
     title = {Axes of {Points} of {Certain} {Linear} {Systems} of {Polarities}},
     journal = {Canadian journal of mathematics},
     pages = {1072--1077},
     year = {1967},
     volume = {19},
     number = {1},
     doi = {10.4153/CJM-1967-097-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-097-1/}
}
TY  - JOUR
AU  - Schuster, Seymour
TI  - Axes of Points of Certain Linear Systems of Polarities
JO  - Canadian journal of mathematics
PY  - 1967
SP  - 1072
EP  - 1077
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-097-1/
DO  - 10.4153/CJM-1967-097-1
ID  - 10_4153_CJM_1967_097_1
ER  - 
%0 Journal Article
%A Schuster, Seymour
%T Axes of Points of Certain Linear Systems of Polarities
%J Canadian journal of mathematics
%D 1967
%P 1072-1077
%V 19
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-097-1/
%R 10.4153/CJM-1967-097-1
%F 10_4153_CJM_1967_097_1

[1] 1. Coxeter, H. S. M., The real projective plane, 2nd ed. (Cambridge, 1955). Google Scholar

[2] 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

Cité par Sources :