Circles and Clifford Algebras |
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Authors: | V. A. Timorin |
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Affiliation: | (1) Independent University of Moscow; University of Toronto, Russia |
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Abstract: | Consider a smooth map of a neighborhood of the origin in a real vector space into a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines passing through the origin to germs of Euclidean circles, or lines, or a point. We prove that under some simple additional assumptions this map takes all lines passing though the origin to the same circles as a Hopf map coming from a representation of a Clifford algebra. We also describe a connection between our result and the Hurwitz–Radon theorem about sums of squares. |
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Keywords: | line circle Hopf map |
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