Magnetic moment of an electron gas on the surface of constant negative curvature

The magnetic moment of an electron gas on the surface of constant negative curvature is investigated. It is shown that the surface curvature leads to the appearance of the region of the monotonic dependence $M(B)$ at low magnetic fields. At high magnetic fields, the dependence of the magnetic moment on a magnetic field is the oscillating one. The effect of the surface curvature is to increase the region of the monotonic dependence of the magnetic moment and to break the periodicity of oscillations of the magnetic moment as a function of an inverse magnetic field.