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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Tohoku Mathematical Journal. Second Series
( Vol. 58 NO.3 / (2006))
A splitting theorem for proper complex equifocal submanifolds
Naoyuki Koike,
Pages. 393-417
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.
Contents 1. Introduction
2. Basic notions and facts
3. The complex Coxeter group associated with a proper anti-Kaehlerian isoparametric submanifold
4. Proof of Theorem 1
5. Proof of Theorem 2
6. The complex Coxeter groups of the principal orbits of actions of Hermann type
Key words Complex equifocal, anti-Kaehlerian isoparametric, complex Coxeter group
Mathmatical Subject Classification 53C40