A SPLITTING THEOREM FOR PROPER COMPLEX EQUIFOCAL SUBMANIFOLDS

• KOIKE NAOYUKI

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

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.

Journal

• Tohoku Mathematical Journal, Second Series

  Tohoku Mathematical Journal, Second Series 58 (3), 393-417, 2006

  Mathematical Institute, Tohoku University

Keywords

• Complex equifocal
• anti-Kaehlerian isoparametric
• complex Coxeter group

Details

• CRID: 1390282680092415104
• NII Article ID: 110004762690
• NII Book ID: AA00863953
• DOI: 10.2748/tmj/1163775137
• ISSN: 2186585X
• ISSN: 00408735
• MRID: 2273277
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed