Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 46, Number 1 (2009), 21-85.
Classification of compact transformation groups on complex quadrics with codimension one orbits
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.
Osaka J. Math., Volume 46, Number 1 (2009), 21-85.
First available in Project Euclid: 25 February 2009
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57S25: Groups acting on specific manifolds
Secondary: 57R22: Topology of vector bundles and fiber bundles [See also 55Rxx]
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