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Circles and Clifford Algebras

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Type
Preprint
Publication Date
Submission Date
Identifiers
arXiv ID: math/0210212
Source
arXiv
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Unknown
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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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