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arXiv · 1910.11273

On Curvature and Torsion in Courant Algebroids

Paolo Aschieri·Francesco Bonechi·Andreas Deser
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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.

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Paolo Aschieri, Francesco Bonechi, Andreas Deser. 2021-02-03. On Curvature and Torsion in Courant Algebroids. https://arxiv.org/abs/1910.11273

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