Integrability Conditions for Generalized Geometric Structures
Published:Dec 30, 2025 08:47
•1 min read
•ArXiv
Analysis
This paper explores integrability conditions for generalized geometric structures (metrics, almost para-complex structures, and Hermitian structures) on the generalized tangent bundle of a smooth manifold. It investigates integrability with respect to two different brackets (Courant and affine connection-induced) and provides sufficient criteria for integrability. The work extends to pseudo-Riemannian settings and discusses implications for generalized Hermitian and Kähler structures, as well as relationships with weak metric structures. The paper contributes to the understanding of generalized geometry and its applications.
Key Takeaways
- •Investigates integrability of generalized geometric structures.
- •Considers integrability with respect to Courant and affine connection brackets.
- •Provides sufficient criteria for integrability.
- •Explores extensions to pseudo-Riemannian settings.
- •Discusses implications for generalized Hermitian and Kähler structures.
- •Describes relationship between generalized metrics and weak metric structures.
Reference
“The paper gives sufficient criteria that guarantee the integrability for the aforementioned generalized structures, formulated in terms of properties of the associated 2-form and connection.”