Hypersurfaces Fixed by Equiaffinities
Canadian mathematical bulletin, Tome 16 (1973) no. 1, pp. 129-131
Voir la notice de l'article provenant de la source Cambridge University Press
In this note we state and prove the following Any equiaffinity acting on the points of an n-dimensional vector space (n ≥2) leaves invariant the members of a one parameter family of hypersurfaces defined by polynomials p(xl...,xn)=c of degree m ≤n.The theorem, restricted to the real plane, appears to have been discovered almost simultaneously by Coxeter [4] and Komissaruk [5]. The former paper presents an elegant geometric argument, showing that the result follows from the converse of Pascal's theorem. The present approach is more closely related to that of [5], in which the transformations are reduced to a canonical form.
Fisher, J. C. Hypersurfaces Fixed by Equiaffinities. Canadian mathematical bulletin, Tome 16 (1973) no. 1, pp. 129-131. doi: 10.4153/CMB-1973-024-x
@article{10_4153_CMB_1973_024_x,
author = {Fisher, J. C.},
title = {Hypersurfaces {Fixed} by {Equiaffinities}},
journal = {Canadian mathematical bulletin},
pages = {129--131},
year = {1973},
volume = {16},
number = {1},
doi = {10.4153/CMB-1973-024-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-024-x/}
}
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