
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 , 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 , which unifies generalized complex (contact) structures on an even(odd)-dimensional manifold.
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