A splitting theorem for equifocal submanifolds in simply connected compact symmetric spaces
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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.References
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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
- 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
- © Copyright 1998 American Mathematical Society
- 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