Hypersurfaces Fixed by Equiaffinities
Keyword(s):
The Real
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In this note we state and prove the followingAny 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.
2019 ◽
Vol 19
(05)
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pp. 2050086
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Keyword(s):
2011 ◽
Vol 85
(1)
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pp. 19-25
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1982 ◽
Vol 25
(2)
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pp. 133-139
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2017 ◽
Vol 83
(12)
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pp. 83-111
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