Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C40, 53C30, 57S25

Retrieve articles in all journals with MSC (1991): 53C40, 53C30, 57S25

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

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia