Jacobi quasi-Nijenhuis Algebroids

TL;DR

This paper introduces Jacobi quasi-Nijenhuis algebroids, generalizing Poisson quasi-Nijenhuis manifolds, and explores their role in generalized complex structures on Courant-Jacobi algebroids, unifying complex and contact structures.

Contribution

It defines Jacobi quasi-Nijenhuis algebroids and studies their application to generalized complex structures on Courant-Jacobi algebroids, extending existing frameworks.

Findings

Unified generalized complex and contact structures on manifolds.

Extended the concept of Poisson quasi-Nijenhuis manifolds to Jacobi algebroids.

Provided new insights into the structure of Courant-Jacobi algebroids.

Abstract

In this paper, for a Jacobi algebroid $A$, by introducing the notion of Jacobi quasi-Nijenhuis algebroids, which is a generalization of Poisson quasi-Nijenhuis manifolds introduced by Sti\'{e}non and Xu, we study generalized complex structures on the Courant-Jacobi algebroid $A\oplus A^*$, which unifies generalized complex (contact) structures on an even(odd)-dimensional manifold.