Connections on Metriplectic Manifolds

2006/05/10 by Daniel Fish, Fish, Daniel
Mathematics · Physics and Astronomy · #53D15 #53D17 #70G45 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53D15 #msc:53D17 #msc:70G45

paper · pdf · doi:10.48550/arxiv.math/0605247

arxiv created 2006/05/10 · openalex publication_date 2006/05/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we discuss conditions under which a linear connection on a manifold equipped with both a symmetric (Riemannian) and a skew-symmetric (almost-symplectic or Poisson) tensor field will preserve both structures.

Citations

• A paradigm for joined Hamiltonian and dissipative systems

Related

• Riemannian manifolds admitting a projective semi-symmetric connection
• A new connection in a Riemannian manifold
• A new look at connections
• Coupling Tensors and Poisson Geometry Near a Single Symplectic Leaf
• Symplectic connections