It is a brief review of a new class of N = 2supersymmetric Landau models which generalize the superplane Landau model by extending it to an arbitrary magnetic field on any two-dimensional manifold M _2. Using an off-shell N = 2 superfield formalism, it is shown that these models are characterized by two independent potentials given on M _2. The relevant Hamiltonians are factorizable and in the special case, when both the Gauss curvature and the magnetic field are constant over M _2, admit infinite series of factorization chains, which implies the integrability of the associated systems. For the particular model with the ?? ~1 bosonic manifold, the spectrum and eigenvectors are explicitly given.
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