On the geometry of compatible Poisson and Riemannian structures
classification
🧮 math.SG
keywords
structuremanifoldspoissonriemannianstructuresadditionahler--poissonalmost
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We consider compatibility conditions between Poisson and Riemannian structures on smooth manifolds by means of a contravariant partially complex structure, or $f$-structure, introducing the notion of (almost) K\"ahler--Poisson manifolds. In addition, we study some of their properties under structure preserving maps and symmetries.
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