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Circles and Clifford Algebras

Vladlen Timorin
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Abstract

Consider a smooth map from a neighborhood of the origin in a real vector space to 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 does. We also describe a connection between our result and the Hurwitz--Radon theorem about sums of squares.

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Vladlen Timorin. 2004-01-29. Circles and Clifford Algebras. https://arxiv.org/abs/math/0210212

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