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math.DG2025
Courant algebroid lifts and curved Courant algebroids
Filip Moučka, Roberto Rubio
We introduce the Courant algebroid lift, a new construction that takes a Courant algebroid together with a vector bundle connection and produces, when the connection is flat in the…
math.DG2025
Symmetric Poisson geometry, totally geodesic foliations and Jacobi-Jordan algebras
Filip Moučka, Roberto Rubio
We introduce symmetric Poisson structures as pairs consisting of a symmetric bivector field and a torsion-free connection satisfying an integrability condition analogous to that in…
math.DG2025
Symmetric Cartan calculus, the Patterson-Walker metric and Killing vector fields
Filip Moučka, Roberto Rubio
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 sym…