  We study symmetry breaking and gap generation for fermions in the 2D space of
constant negative curvature (the Lobachevsky plane) in an external covariantly
constant magnetic field in a four-fermion model. It is shown that due to the
magnetic and negative curvature catalysis phenomena the critical coupling
constant is zero and there is a symmetry breaking condensate in the chiral
limit even in free theory. We analyze solutions of the gap equation in the
cases of zero, weak, and strong magnetic fields. As a byproduct we calculate
the density of states and the Hall conductivity for noninteracting fermions
that may be relevant for studies of graphene.
