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arXiv · 2307.12739

Riemann-Poisson and K\"ahler-Poisson complex manifolds and structures

Ibrahima Hamidine·ALi Mahamane Saminou
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Abstract

In this paper we consider structures of complex Poisson brackets on the space of smooth functions in a $n$-dimensional complex manifold generated by the $(1,1)$-form $d=\partial+\overline{\partial}$-closed and non-degenerate (with non-holomorphic and non-antiholomorphic coefficients). In this case, we have view the compatibility between complex Poisson and Riemannian structures and an example is giving in $\C^\ast$.

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Ibrahima Hamidine, ALi Mahamane Saminou. 2023-07-24. Riemann-Poisson and K\"ahler-Poisson complex manifolds and structures. https://arxiv.org/abs/2307.12739

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