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Holomorphic Jacobi Manifolds

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arxiv 1609.07737 v2 pith:BXCC436V submitted 2016-09-25 math.DG math.CVmath.SG

Luca Vitagliano , Aïssa Wade This is my paper · ORCID
classification math.DGmath.CVmath.SG
keywords holomorphicjacobimanifoldsstructurespoissonbundlescasescertain
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In this paper, we develop holomorphic Jacobi structures. Holomorphic Jacobi manifolds are in one-to-one correspondence with certain homogeneous holomorphic Poisson manifolds. Furthermore, holomorphic Poisson manifolds can be looked at as special cases of holomorphic Jacobi manifolds. We show that holomorphic Jacobi structures yield a much richer framework than that of holomorphic Poisson structures. We also discuss the relationship between holomorphic Jacobi structures, generalized contact bundles and Jacobi-Nijenhuis structures.

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  1. On Homogeneous K\"ahler Manifolds

    math.DG 2026-08 conditional novelty 6.0 of 10

    Homogeneous Kähler structures on principal R^×-bundles reduce to Sasakian structures exactly when the Euler vector field is pre-geodesic and the line bundle is oriented, and the same dictionary covers co-Kähler struct...

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