Constructions of smooth \(SU(p, q)\)-actions on the projective space \(\mathbf P^{p + q - 1}_{\mathbb C}\) with \(m\) closed and \(m + 1\) open orbits
type: Item
instance of: scholarly article
title: Constructions of smooth \(SU(p, q)\)-actions on the projective space \(\mathbf P^{p + q - 1}_{\mathbb C}\) with \(m\) closed and \(m + 1\) open orbits
zbMATH Open document ID: 1446.57027
author: Kazuo Mukōyama
author: Tomoaki Ono
author: Kenji Takei
published in: Tokyo Journal of Mathematics
publication date: 2020-08-03T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.tjm/1566612099
review text: The authors consider actions of generalized special unitary groups on complex projective spaces. Assume \(p,q\geq 3\) and \(m>0\). The main result says that there exist uncountably many equivalence classes of smooth \(SU(p,q)\)-actions on \({\mathbf{P}}^{p+q-1}_{\mathbb{C}}\) with \(m\) closed and \(m+1\) open orbits. It then follows that there also exist uncountably many equivalence classes of smooth \(SU(p,q)\)-actions on the sphere \({\mathbb{S}}^{2p+2q-1}\) with \(m\) closed and \(m+1\) open orbits. The proof is based on constructing triples of real valued smooth functions on a circle satisfying specific conditions.
reviewed by: Marja Kankaanrinta
Mathematics Subject Classification ID: 57S20
zbMATH DE Number: 7227183
zbMATH Keywords: special unitary group
zbMATH Keywords: smooth action
zbMATH Keywords: complex projective space
zbMATH Keywords: sphere
MaRDI profile type: Publication
OpenAlex ID: W2970043438
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DOI: 10.3836/TJM/1502179299
description: scientific article; zbMATH DE number 7227183