A splitting theorem for equifocal submanifolds in simply connected compact symmetric spaces

Author:
Heiko Ewert

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2443-2452

MSC (1991):
Primary 53C40; Secondary 53C30, 57S25

DOI:
https://doi.org/10.1090/S0002-9939-98-04328-7

MathSciNet review:
1451798

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Abstract: A submanifold in a symmetric space is called equifocal if it has a globally flat abelian normal bundle and its focal data is invariant under normal parallel transportation. This is a generalization of the notion of isoparametric submanifolds in Euclidean spaces. To each equifocal submanifold, we can associate a Coxeter group, which is determined by the focal data at one point. In this paper we prove that an equifocal submanifold in a simply connected compact symmetric space is a non-trivial product of two such submanifolds if and only if its associated Coxeter group is decomposable. As a consequence, we get a similar splitting result for hyperpolar group actions on compact symmetric spaces. These results are an application of a splitting theorem for isoparametric submanifolds in Hilbert spaces by Heintze and Liu.

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Additional Information

**Heiko Ewert**

Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts 02115

Address at time of publication:
Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany

Email:
ewert@mi.uni-koeln.de

DOI:
https://doi.org/10.1090/S0002-9939-98-04328-7

Received by editor(s):
May 28, 1996

Received by editor(s) in revised form:
January 22, 1997

Additional Notes:
Research supported in part by DAAD and Northeastern University

Communicated by:
Christopher Croke

Article copyright:
© Copyright 1998
American Mathematical Society