Quantum Hall effect on the Lobachevsky plane

The Hall conductivity of an electron gas on the surface of constant negative curvature (the Lobachevsky plane) in the presence of an orthogonal magnetic field is investigated. It is shown that the surface curvature decreases the quantum Hall plateau widths and shifts the steps in the Hall conductivity to higher magnetic fields (or to lower values of the chemical potential). An increase of temperature results in smearing of the steps