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.

中文翻译：

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关于courant代数的曲率和扭转

我们研究了Q流形（微分梯度流形）的曲率和扭转的渐变几何角度。特别是，我们获得了自然的库仑代数曲率和扭转的几何渐变定义，正确地限制了狄拉克结构。根据辅助仿射连接K，我们介绍了库仑代数连接的K曲率和K扭转。这些是身体上的常规张量。最后，我们计算它们的Ricci和标量曲率。