Tohoku Mathematical Journal

A splitting theorem for proper complex equifocal submanifolds

Naoyuki Koike

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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

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

First available in Project Euclid: 17 November 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Complex equifocal anti-Kaehlerian isoparametric complex Coxeter group


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.

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