3 papers
math.SG2026
On the Dirac complement problem
Tom Ariel, Roberto Rubio, Marco Zambon
The existence of a Dirac complement for a given Dirac structure is a central question in the structure theory of Courant algebroids and the deformation theory of Dirac structures.…
math.DG2025
Flat Generalized Connections on Courant Algebroids
Gil R. Cavalcanti, Jaime Pedregal, Roberto Rubio
We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We f…
math.DG2024
On the Equivalence of Generalized Ricci Curvatures
Gil R. Cavalcanti, Jaime Pedregal, Roberto Rubio
We prove the equivalence between the several notions of generalized Ricci curvature found in the literature. As an application, we characterize when the total generalized Ricci ten…