Riemann-Poisson and Kähler-Poisson complex manifolds and structures

2023/07/24 by Ibrahima Hamidine, Hamidine, Ibrahima, ALi Mahamane Saminou +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2307.12739

openalex publication_date 2023/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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=∂+∂-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^∗.

Related

• On the geometry of compatible Poisson and Riemannian structures
• Theorem of existence and completeness for holomorphic Poisson structures
• On the geometry of Kähler-Poisson structures
• On the geometry of complex Poisson bivectors
• Local structure of generalized complex manifolds