Circles and Clifford Algebras

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dc.creatorTimorin, Vladlen
dc.date2002-10-15
dc.date2004-01-29
dc.date.accessioned2026-07-07T04:51:55Z
dc.date.available2026-07-07T04:51:55Z
dc.descriptionConsider 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.
dc.description12 pages; to appear in Funct. Anal. and its Appl.; v4: minor corrections
dc.identifierhttps://arxiv.org/abs/math/0210212
dc.identifierhttp://arxiv.org/abs/math/0210212
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65286
dc.subjectMetric Geometry
dc.subjectDifferential Geometry
dc.subject15A66; 51M04
dc.titleCircles and Clifford Algebras
dc.typetext

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