We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.
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