## Tokyo Journal of Mathematics

### Homogeneity of Infinite Dimensional Anti-Kaehler Isoparametric Submanifolds II

Naoyuki KOIKE

#### Abstract

In this paper, we prove that, if a full irreducible infinite dimensional anti-Kaehler isoparametric submanifold of codimension greater than one has $J$-diagonalizable shape operators, then it is an orbit of the action of a Banach Lie group generated by one-parameter transformation groups induced by holomorphic Killing vector fields defined entirely on the ambient Hilbert space.

#### Article information

Source
Tokyo J. Math., Volume 40, Number 2 (2017), 301-337.

Dates
First available in Project Euclid: 9 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1515466828

Digital Object Identifier
doi:10.3836/tjm/1502179231

Mathematical Reviews number (MathSciNet)
MR3743722

Zentralblatt MATH identifier
1301.53052

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]

#### Citation

KOIKE, Naoyuki. Homogeneity of Infinite Dimensional Anti-Kaehler Isoparametric Submanifolds II. Tokyo J. Math. 40 (2017), no. 2, 301--337. doi:10.3836/tjm/1502179231. https://projecteuclid.org/euclid.tjm/1515466828

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