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{1163775137,
author = {Koike, Naoyuki},
title = {A splitting theorem for proper complex equifocal submanifolds},
journal = {Tohoku Math. J. (2)},
volume = {58},
number = {1},
year = {2006},
pages = { 393-417},
language = {en},
url = {http://dml.mathdoc.fr/item/1163775137}
}
Koike, Naoyuki. A splitting theorem for proper complex equifocal submanifolds. Tohoku Math. J. (2), Tome 58 (2006) no. 1, pp. 393-417. http://gdmltest.u-ga.fr/item/1163775137/