Asian Journal of Mathematics

On Non-existenceness of Equifocal Submanifolds with Non-flat Section

Naoyuki Koike

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Abstract

We first prove a certain kind of splitting theorem for an equifocal submanifold with non-flat section in a simply connected symmetric space of compact type, where an equifocal submanifold means a submanifold with parallel focal structure. By using the splitting theorem, we prove that there exists no equifocal submanifold with non-flat section in an irreducible simply connected symmetric space of compact type whose codimension is greater than the maximum of the multiplicities of roots of the symmetric space or the maximum added one. In particular, it follows that there exists no equifocal submanifold with non-flat section in some irreducible simply connected symmetric spaces of compact type and that there exists no equifocal submanifold with non-flat section in simply connected compact simple Lie group whose codimension is greater than two.

Article information

Source
Asian J. Math., Volume 12, Number 4 (2008), 421-442.

Dates
First available in Project Euclid: 20 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1235140166

Mathematical Reviews number (MathSciNet)
MR2481684

Zentralblatt MATH identifier
05554935

Subjects
Primary: 53C40: Global submanifolds [See also 53B25] 53C35: Symmetric spaces [See also 32M15, 57T15]

Keywords
Equifocal submanifold polar action

Citation

Koike, Naoyuki. On Non-existenceness of Equifocal Submanifolds with Non-flat Section. Asian J. Math. 12 (2008), no. 4, 421--442. https://projecteuclid.org/euclid.ajm/1235140166


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