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June 2005 Complex Equifocal Submanifolds and Infinite Dimensional Anti-Kaehlerian Isoparametric Submanifolds
Naoyuki KOIKE
Tokyo J. Math. 28(1): 201-247 (June 2005). DOI: 10.3836/tjm/1244208289

Abstract

In a symmetric space of non-compact type, we have recently defined the notion of a complex equifocal submanifold. In this paper, we introduce the notion of an infinite dimensional anti-Kaehlerian isoparametric submanifold. We show that the investigation of complete real analytic complex equifocal submanifolds is reduced to that of infinite dimensional anti-Kaehlerian isoparametric submanifolds. Also, we show that an infinite dimensional anti-Kaehlerian isoparametric submanifold is multi-foliated by complex spheres (or complex affine subspaces) and that the main part of the focal set of the submanifold at each point consists of some complex hyperplanes in the normal space.

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Naoyuki KOIKE. "Complex Equifocal Submanifolds and Infinite Dimensional Anti-Kaehlerian Isoparametric Submanifolds." Tokyo J. Math. 28 (1) 201 - 247, June 2005. https://doi.org/10.3836/tjm/1244208289

Information

Published: June 2005
First available in Project Euclid: 5 June 2009

zbMATH: 1089.53037
MathSciNet: MR2149633
Digital Object Identifier: 10.3836/tjm/1244208289

Rights: Copyright © 2005 Publication Committee for the Tokyo Journal of Mathematics

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Vol.28 • No. 1 • June 2005
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