Geometrothermodynamics in Horava-Lifshitz gravity

We investigate the thermodynamic geometries of the most general static, spherically symmetric, topological black holes of the Horava-Lifshitz gravity. In particular, we show that a Legendre invariant metric derived in the context of geometrothermodynamics for the equilibrium manifold correctly reproduces the phase transition structure of these black holes. Moreover, the limiting cases in which the mass, entropy or Hawking temperature vanish are also accompanied by curvature singularities which indicate the limit of applicability of the thermodynamics and geometrothermodynamics of black holes. The Einstein limit and the case of a black hole with a flat horizon are also investigated.