Some examples of global Poisson structures on $S^4
Kodai Math. J. 42 (2019), no. 2, 223--246 A Poisson structure is represented by a bivector whose Schouten bracket vanishes. We study a global Poisson structure on $S^4$ associated with a holomorphic Poisson structure on $\mathbb{CP}^3$. The space of the Poisson structures on $S^4$ is a real algebrai...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
02.10.2015
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Subjects | |
Online Access | Get full text |
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Summary: | Kodai Math. J. 42 (2019), no. 2, 223--246 A Poisson structure is represented by a bivector whose Schouten bracket
vanishes. We study a global Poisson structure on $S^4$ associated with a
holomorphic Poisson structure on $\mathbb{CP}^3$. The space of the Poisson
structures on $S^4$ is a real algebraic variety in the space of holomorphic
Poisson structures on $\mathbb{CP}^3$. We generalize it to $\mathbb{HP}^n$ by
using the twistor method. Furthermore, we provide examples of Poisson
structures on $S^4$ associated with codimension one holomorphic foliations of
degree 2 on $\mathbb{CP}^3$. |
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DOI: | 10.48550/arxiv.1510.00497 |