A splitting theorem for proper complex equifocal submanifolds

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概要

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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.

著者

• Koike Naoyuki

  Department of Mathematics, Faculty of Science, Tokyo University of Science

• Koike Naoyuki

  Department Of Material And Life Chemistry Faculty Of Engineering Kanagawa University

• Koike Naoyuki

  Department Of Mathematics Faculty Of Science Tokyo University Of Science

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