  The thermodynamics of the Schwarzschild-AdS black hole is reformulated within
the context of the recently developed formalism of geometrothermodynamics
(GTD). Different choices of the metric in the equilibrium states manifold are
used in order to reproduce the Hawking-Page phase transition as a divergence of
the thermodynamical curvature scalar. We show that the enthalpy and total
energy representations of GTD does not reproduce the transition while the
entropy rep- resentation gives the expected behavior.
