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Holomorphic Jacobi Manifolds and Holomorphic Contact Groupoids

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arxiv 1710.03300 v2 pith:AP45IO3M submitted 2017-10-09 math.DG math.CVmath.SG

Luca Vitagliano , Aïssa Wade This is my paper · ORCID
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keywords holomorphicjacobigroupoidsmanifoldscontactcomplexhomogeneouspart
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This is the second part of a series of two papers dedicated to a systematic study of holomorphic Jacobi structures. In the first part, we introduced and study the concept of a holomorphic Jacobi manifold in a very natural way as well as various tools. In the present paper, we solve the integration problem for holomorphic Jacobi manifolds by proving that they integrate to complex contact groupoids. A crucial tool in our proof is what we call the "homogenization scheme", which allows us to identify holomorphic Jacobi manifolds with homogeneous holomorphic Poisson manifolds and holomorphic contact groupoids with homogeneous complex symplectic groupoids.

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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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