Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 58, Number 3 (2006), 393-417.
A splitting theorem for proper complex equifocal submanifolds
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.
Tohoku Math. J. (2), Volume 58, Number 3 (2006), 393-417.
First available in Project Euclid: 17 November 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C40: Global submanifolds [See also 53B25]
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