Ricci tensor in graded geometry

Abstract

We define the notion of the Ricci tensor for NQ symplectic manifolds of degree 2 and show that it corresponds to the standard generalized Ricci tensor on Courant algebroids. We use an appropriate notion of connections compatible with the generalized metric on the graded manifold.

arXiv comment6 pages, minor changes, added references, accepted manuscript version

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• Super AKSZ construction, integral forms, and the 2-dimensional $\mathcal{N}=(1,1)$ sigma model