Papers

Here you can find our papers and preprints:

• Flat Generalized Connections on Courant Algebroids
  Paper by G. Cavalcanti, J. Pedregal and R. Rubio. Abstract: 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 find that the building blocks for such flat transitive Courant algebroids are compact simple Lie groups. Further, we give a description… Read more: Flat Generalized Connections on Courant Algebroids
• Symmetric Cartan calculus, the Patterson-Walker metric and symmetric cohomology
  Paper by F. Moučka and R. Rubio. Abstract: We develop symmetric Cartan calculus, an analogue of classical Cartan calculus for symmetric differential forms. We first show that the analogue of the exterior derivative, the symmetric derivative, is not unique and its different choices are parametrized by torsion-free affine connections. We use a choice of symmetric… Read more: Symmetric Cartan calculus, the Patterson-Walker metric and symmetric cohomology
• On the Equivalence of Generalized Ricci Curvatures
  Paper by G. Cavalcanti, J. Pedregal and R. Rubio. Abstract: 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 tensor is symmetric. Find it on the arXiv (2406.06695). To appear in Proc. Amer. Math. Soc.
• New geometric structures on 3-manifolds: surgery and generalized geometry
  Paper by J. Porti and R. Rubio. Abstract: Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common generalization of these two structures: B3-generalized complex structures. We prove that any closed orientable 3-manifold admits… Read more: New geometric structures on 3-manifolds: surgery and generalized geometry