We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shifted tangent bundle. We view this construction as a generalization of Sasaki’s construction of a Riemannian metric on the tangent bundle of a Riemannian manifold.

中文翻译：

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反切丛上的超 Sasaki 度量

我们展示了如何将流形上的黎曼度量和几乎辛形式提升到称为反切线或移位切线丛的规范相关超流形上的黎曼结构。我们将这种构造视为 Sasaki 在黎曼流形的切丛上构造黎曼度量的推广。