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Annals of Mathematics, II. SeriesVol. 149, No. 1, pp. 149-181 (1999) |
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Homogeneity of infinite dimensional isoparametric submanifoldsErnst Heintze and Xiaobo LiuReview from Zentralblatt MATH: The main result of the paper is the following remarkable Theorem. Let $M$ be a complete, connected, irreducible isoparametric submanifold in a Hilbert space $V$. Assume that the set of all the curvature normals of $M$ at some point is not contained in any affine line. Then, $M$ is extrinscially homogeneous in the Hilbert space $V$. The finite dimensional case of this theorem was first proved by the reviewer [Ann. Math., II. Ser. 133, 429-446 (1991; Zbl 0845.53040)]. It is very likely that the main result of the paper under review can be used to prove a homogeneity theorem for equifocal submanifolds. Reviewed by G.Thorbergsson Keywords: isoparametric submanifolds; proper Fredholm submanifolds in Hilbert spaces; homogeneity theorem; equifocal submanifolds Classification (MSC2000): 53C40 53C30 Full text of the article:
Electronic fulltext finalized on: 18 Aug 2001. This page was last modified: 21 Jan 2002.
© 2001 Johns Hopkins University Press
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