Tohoku Mathematical Journal
2006
September
SECOND SERIES VOL. 58, NO. 3

Tohoku Math. J.
58 (2006), 393-417

Title A SPLITTING THEOREM FOR PROPER COMPLEX EQUIFOCAL SUBMANIFOLDS

Author Naoyuki Koike

(Received November 4, 2004, revised December 13, 2005)
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.

2000 Mathematics Subject Classification. 53C40.
Key words and phrases. Complex equifocal, anti-Kaehlerian isoparametric, complex Coxeter group.

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