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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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: http://dx.doi.org/10.1090/S0002-9939-98-04328-7
PII: S 0002-9939(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