The geometric framework of Double Field Theory (DFT) can be constructed on a para-Hermitian manifold. The canonical, generalized-metric connections and the global expression of the corresponding covariant derivative, a generalization of the kinematical structure of DFT, generalized curvature, a corresponding generalized Lie derivative for the Leibniz algebroid on the tangent bundle are constructed. In the present paper, we construct the similar action of DFT and para-Hermitian manifolds on ρ-commutative algebras and extend the above notions on it.

中文翻译：

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ρ-交换代数上的广义运动学

双场论 (DFT) 的几何框架可以构建在准厄米流形上。构建了规范的广义度量连接和相应协变导数的全局表达式、DFT 运动学结构的推广、广义曲率、切丛上莱布尼茨代数的相应广义李导数。在本文中，我们在 ρ-交换代数上构造了 DFT 和准厄米流形的类似作用，并在上面扩展了上述概念。