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June 2019 Some examples of global Poisson structures on $S^4$
Takayuki Moriyama, Takashi Nitta
Kodai Math. J. 42(2): 223-246 (June 2019). DOI: 10.2996/kmj/1562032829

Abstract

A Poisson structure is a bivector whose Schouten bracket vanishes. We study a global Poisson structure on $S^4$ associated with a holomorphic Poisson structure on $\mathbf{CP}^3$. The space of such Poisson structures on $S^4$ is realised as a real algebraic variety in the space of holomorphic Poisson structures on $\mathbf{CP}^3$. We generalize the result to the higher dimensional case $\mathbf{HP}^n$ by the twistor method. It is known that a holomorphic Poisson structure on $\mathbf{CP}^3$ corresponds to a codimension one holomorphic foliation and the space of these foliations of degree 2 has six components. In this paper we provide examples of Poisson structures on $S^4$ associated with these components.

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Takayuki Moriyama. Takashi Nitta. "Some examples of global Poisson structures on $S^4$." Kodai Math. J. 42 (2) 223 - 246, June 2019. https://doi.org/10.2996/kmj/1562032829

Information

Published: June 2019
First available in Project Euclid: 2 July 2019

zbMATH: 07108011
MathSciNet: MR3981305
Digital Object Identifier: 10.2996/kmj/1562032829

Rights: Copyright © 2019 Tokyo Institute of Technology, Department of Mathematics

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Vol.42 • No. 2 • June 2019
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