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.
