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

Author:

Ibrahima Hamidine, ALi Mahamane Saminou

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Complex Variables (math.CV)

journal:

date:

2023-07-23 16:00:00

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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