## Osaka Journal of Mathematics

### Classification of compact transformation groups on complex quadrics with codimension one orbits

Shintarô Kuroki

#### Abstract

Let $G$ be a compact connected Lie group and $M$ a rational cohomology complex quadric of real dimension divisible by $4$ (where $\dim M\neq 4$). The aim of this paper is to classify pairs $(G,M)$ such that $G$ acts smoothly on $M$ with codimension one principal orbits. There exist eight such pairs up to essential isomorphism. The underlying manifold $M$ is diffeomorphic to the genuine complex quadric except one pair.

#### Article information

Source
Osaka J. Math., Volume 46, Number 1 (2009), 21-85.

Dates
First available in Project Euclid: 25 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1235574038

Mathematical Reviews number (MathSciNet)
MR2531140

Zentralblatt MATH identifier
1170.57028

#### Citation

Kuroki, Shintarô. Classification of compact transformation groups on complex quadrics with codimension one orbits. Osaka J. Math. 46 (2009), no. 1, 21--85. https://projecteuclid.org/euclid.ojm/1235574038

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