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On Curvature and Torsion in Courant Algebroids (1910.11273v2)
Published 23 Oct 2019 in math.DG, hep-th, math-ph, and math.MP
Abstract: We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly restrict to Dirac structures. Depending on an auxiliary affine connection K, we introduce the K-curvature and K-torsion of a Courant algebroid connection. These are conventional tensors on the body. Finally, we compute their Ricci and scalar curvature.