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A generalization of Cartan's theorem on isoparametric cubics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2010 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 138, no 8, 2889-2895 p.Article in journal (Refereed) Published
Abstract [en]

We generalize the well-known result of E. Cartan on isoparametric cubics by showing that a homogeneous cubic polynomial solution of the eiconal equation vertical bar del f vertical bar(2)= 9 vertical bar x vertical bar(4) must be rotationally equivalent to either x(n)(3) - 3x(n) (x(1)(2) + ... + x(n-1)(2)) or to one of four exceptional Cartan cubic polynomials in dimensions n = 5,8,14,26.

Place, publisher, year, edition, pages
2010. Vol. 138, no 8, 2889-2895 p.
Keyword [en]
Cartan's theorem, division algebras, composition formulas, quadratic maps, eiconal equation, minimal cubic cones
National Category
URN: urn:nbn:se:kth:diva-29455DOI: 10.1090/S0002-9939-10-10385-2ISI: 000280305000022ScopusID: 2-s2.0-77952032210OAI: diva2:395988
QC 20110208Available from: 2011-02-08 Created: 2011-02-02 Last updated: 2011-02-08Bibliographically approved

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Tkachev, Vladimir
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Mathematics (Dept.)
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