Isoparametric triple systems of FKM-type. I
type: Item
instance of: scholarly article
title: Isoparametric triple systems of FKM-type. I
zbMATH Open document ID: 0531.53048
DOI: 10.1007/BF02941319
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1983-01-01T00:00:00Z
review text: [For the second part see the next review.] The largest and most important known class of isoparametric hypersurfaces in spheres are those considered in \textit{D. Ferus, H. Karcher, H. F. Münzner}, Math. Z. 177, 479-502 (1982; Zbl 0443.53037). The authors have developed an algebraic approach describing all isoparametric hypersurfaces in a sphere with 4 distinct principal curvatures by isoparametric triple systems [Tôhoku Math. J. 35, 187-224 (1983; Zbl 0507.53038) and ibid., 225-248 (1983; Zbl 0507.53039)]. In the present paper this general approach is specialized to those isoparametric triple systems which correspond to the surfaces constructed by D. Ferus, H. Karcher and H. F. Münzner and which are called of FKM-type. In particular, tripotents and their Peirce decompositions are described which are the most important tool in the general theory. Moreover, an intrinsic characterization for an isoparametric triple system to be of FKM-type is obtained. The results lay the foundations for the following 2 parts and are also used in the classification of isoparametric hypersurfaces of ''algebra type'', first studied by \textit{H. Ozeki} and \textit{M. Takeuchi} [ibid. 27, 515-559 (1975; Zbl 0359.53011) and ibid. 28, 7-55 (1976; Zbl 0359.53012)] and classified by the authors [Osaka J. Math. 20, 145-176 (1983)].
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 17A40
zbMATH DE Number: 3842677
zbMATH Keywords: FKM-triples
zbMATH Keywords: Clifford representations
zbMATH Keywords: isoparametric hypersurfaces
zbMATH Keywords: isoparametric triple systems
author: Josef F. Dorfmeister
author: Erhard Neher
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02941319
OpenAlex ID: W3021244363
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description: scientific article; zbMATH DE number 3842677