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June 2020 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
Kazuo MUKŌYAMA, Tomoaki ONO, Kenji TAKEI
Tokyo J. Math. 43(1): 137-161 (June 2020). DOI: 10.3836/tjm/1502179299

Abstract

There is the close relation between smooth $SU(p,q)$-actions on ${\mathbf P}^{p+q-1}_{\mathbb C}$ and triples of smooth functions satisfying four conditions. To construct smooth $SU(p,q)$-actions on ${\mathbf P}^{p+q-1}_{\mathbb C}$, we construct triples of smooth functions satisfying four conditions. As a result, we can show that for given positive integer $m$ there exist uncountably infinite equivalence classes of smooth $SU(p,q)$-actions on ${\mathbf P}^{p+q-1}_{\mathbb C}$ with $m$ closed and $m+1$ open orbits, and furthermore we have new smooth $SU(p,q)$-actions on $S^{2p+2q-1}$ with $m$ closed and $m+1$ open orbits.

Citation

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Kazuo MUKŌYAMA. Tomoaki ONO. Kenji TAKEI. "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." Tokyo J. Math. 43 (1) 137 - 161, June 2020. https://doi.org/10.3836/tjm/1502179299

Information

Published: June 2020
First available in Project Euclid: 24 August 2019

zbMATH: 07227183
MathSciNet: MR4121791
Digital Object Identifier: 10.3836/tjm/1502179299

Subjects:
Primary: 57S20

Rights: Copyright © 2020 Publication Committee for the Tokyo Journal of Mathematics

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Vol.43 • No. 1 • June 2020
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