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Homogeneity of infinite dimensional isoparametric submanifolds

Ernst Heintze·Xiaobo Liu
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Abstract

A subset S of a Riemannian manifold N is called extrinsically homogeneous if S is an orbit of a subgroup of the isometry group of N. Thorbergsson proved the remarkable result that every complete, connected, full, irreducible isoparametric submanifold of a finite dimensional Euclidean space of rank at least 3 is extrinsically homogeneous. This result, combined with results of Palais-Terng and Dadok, finally classified irreducible isoparametric submanifolds of a finite dimensional Euclidean space of rank at least 3. While Thorbergsson's proof used Tits buildings, a simpler proof without using Tits buildings was given by Olmos. The main purpose of this paper is to extend Thorbergsson's result to the infinite dimensional case.

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Ernst Heintze, Xiaobo Liu. 1999-01-01. Homogeneity of infinite dimensional isoparametric submanifolds. https://arxiv.org/abs/math/9901150

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