In the framework of the method of geometrothermodynamics, in present work, we studied the properties of equilibrium manifold of the system with zero-sound predicted by the holographic duality method. The results are invariant under the Legendre transformations, i.e. independent of the choice of thermodynamic potential. For the systems under consideration, the corresponding metrics, determinants of metrics and scalar curvatures are calculated, and their properties are also described. Using the holographic approach, a new type of quantum liquid was discovered. The heat capacity of the liquid obtained in this work at low temperatures depends on the temperature ∼ T6. Entropy, which depends on temperature and baryom density, was taken as the thermodynamic potential. 3-dimensional obtained that clearly show at which values of thermodynamic variables scalar curvatures tend to infinity or to zero, which indicates possible phase transitions and possible compensation of interactions by quantum effects, respectively. It is shown that both variants of metrics in this case lead to the same conclusion regarding the location of possible phase transition lines in the considered holographic system with zero sound.