Tohoku Mathematical Journal

A splitting theorem for proper complex equifocal submanifolds

Naoyuki Koike

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Abstract

In this paper, we define the notion of the complex Coxeter group associated with a proper complex equifocal submanifold in a symmetric space of non-compact type. We prove that a proper complex equifocal submanifold is decomposed into a non-trivial (extrinsic) product of two such submanifolds if and only if its associated complex Coxeter group is decomposable. Its proof is performed by showing a splitting theorem for an infinite-dimensional proper anti-Kaehlerian isoparametric submanifold.

Article information

Source
Tohoku Math. J. (2), Volume 58, Number 3 (2006), 393-417.

Dates
First available in Project Euclid: 17 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1163775137

Digital Object Identifier
doi:10.2748/tmj/1163775137

Mathematical Reviews number (MathSciNet)
MR2273277

Zentralblatt MATH identifier
1116.53033

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]

Keywords
Complex equifocal anti-Kaehlerian isoparametric complex Coxeter group

Citation

Koike, Naoyuki. A splitting theorem for proper complex equifocal submanifolds. Tohoku Math. J. (2) 58 (2006), no. 3, 393--417. doi:10.2748/tmj/1163775137. https://projecteuclid.org/euclid.tmj/1163775137


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