Holomorphic Jacobi Manifolds and Holomorphic Contact Groupoids

Abstract

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.

v2: 46 pages. Terminology changed from "complex contact manifold" to "holomorphic contact manifold" according to a request of the referee. Other minor changes. Comments still welcome!

References in corpus (2)

• Poisson Quasi-Nijenhuis Manifolds
• On local integration of Lie brackets

Cited by in corpus (8)

• Contact geometry and thermodynamics of black holes in AdS spacetimes
• Jacobi sigma models
• Contact Dual Pairs
• On Locally Conformally Cosymplectic Hamiltonian Dynamics and Hamilton-Jacobi Theory
• Generalized virial theorem for contact Hamiltonian systems
• Topological and dynamical aspects of Jacobi sigma models
• Homogeneous G-structures
• Jacobi Geometry and Hamiltonian Mechanics: the Unit-Free Approach