Holomorphic Jacobi Manifolds
Differential Geometry
2020-02-07 v2 Complex Variables
Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.1609.07737,
title = {Holomorphic Jacobi Manifolds},
author = {Luca Vitagliano and Aïssa Wade},
journal= {arXiv preprint arXiv:1609.07737},
year = {2020}
}
Comments
v2: final version, 33 pages, accepted for publication on IJM. Comments welcome!