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Annals of Mathematics, II. Series, Vol. 149, No. 1, pp. 149-181, 1999
EMIS ELibM Electronic Journals Annals of Mathematics, II. Series
Vol. 149, No. 1, pp. 149-181 (1999)

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Homogeneity of infinite dimensional isoparametric submanifolds

Ernst Heintze and Xiaobo Liu

Review 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.

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