Holomorphic Jacobi Manifolds

TL;DR

This paper introduces holomorphic Jacobi structures, establishing their correspondence with homogeneous holomorphic Poisson manifolds and exploring their richer geometric framework and relationships with other structures.

Contribution

It develops the theory of holomorphic Jacobi manifolds and clarifies their connection to holomorphic Poisson and contact structures, expanding the geometric understanding.

Findings

Holomorphic Jacobi manifolds correspond to certain homogeneous holomorphic Poisson manifolds.

Holomorphic Jacobi structures form a richer framework than holomorphic Poisson structures.

Connections between holomorphic Jacobi structures, contact bundles, and Jacobi-Nijenhuis structures are established.

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.