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arXiv · 1510.00497

Some examples of global Poisson structures on $S^4$

Takayuki Moriyama·Takashi Nitta
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Abstract

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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Takayuki Moriyama, Takashi Nitta. 2017-10-27. Some examples of global Poisson structures on $S^4$. https://arxiv.org/abs/1510.00497

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