The thermodynamic geometry formalism is applied to strongly interacting matter to estimate the deconfinement temperature. The curved thermodynamic metric for Quantum Chromodynamics (QCD) is evaluated on the basis of lattice data, whereas the hadron resonance gas model is used for the hadronic sector. Since the deconfinement transition is a crossover, the geometric criterion used to define the (pseudo-)critical temperature, as a function of the baryonchemical potential µ B , is R(T, µ B ) = 0, where R is the scalar curvature. The (pseudo-)critical temperature, T c , resulting from QCD thermodynamic geometry is in good agreement with lattice and phenomenological freeze-out temperature estimates. The crossing temperature, T h , evaluated by the hadron resonance gas, which suffers of some model dependence, is larger than T c (about 20%) signaling remnants of confinement above the transition.PACS numbers:

The application of Riemannian geometry to the analysis of the equilibrium thermodynamics in Quantum Chromodynamics (QCD) at finite temperature and baryon density gives a new method to evaluate the critical temperature, T c , of the deconfinement transition. In the confined phase, described by the thermodynamic geometry of the Hadron Resonance Gas, the estimate of T c turns out completely consistent with lattice QCD simulations of the quark-gluon plasma phase if the hadron excluded volume and the interaction effects are taken into account.