Using the most general higher-derivative field redefinitions for the closed spacetime manifolds, we show that the tree-level couplings of the metric, $B$-field and dilaton at orders $\\\\alpha\\\'^2$ and $\\\\alpha\\\'^3$ that have been recently found by the T-duality, can be written in a particular scheme in terms of the torsional Riemann curvature $\\\\cR$ and the torsion tensor $H$. The couplings at order $\\\\alpha\\\'^2$ have structures $\\\\cR^3, H^2 \\\\cR^2$, $H^6$, and the couplings at order $\\\\alpha\\\'^3$ have only structures $\\\\cR^4$, $H^2\\\\cR^3$. Replacing $\\\\cR$ with the ordinary Riemann curvature, the couplings in the structure $H^2\\\\cR^3$ reproduce the couplings found in the literature by the S-matrix method.

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