2025/01/07 by Aidan Patterson, Patterson, Aidan
Mathematics · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Rings, Modules, and Algebras #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2501.03519
openalex publication_date 2025/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost para-complex structure, and use this to define a notion of para-holomorphic algebroid. We investigate connections on para-holomorphic algebroids and determine an appropriate sense in which they can be para-complex. Finally, we show through a series of examples how the theory of exact para-holomorphic algebroids with a para-complex connection is a generalization of both para-Kähler geometry and the theory of Poisson-Lie groups.