  Some magnetic phenomena in correlated electron systems were recently shown to
be described in the continuum limit by a class of sigma models which present a
U(1) Hopf fibration over CP(1). In this paper we study a generalization of such
models with a target space given by a U(1) fibration over Grassmannian
manifolds, of which CP($N-1$) is a special case. The metric of our target space
is shown to be left-symmetric which implies that it is fully parametrized by
two constants: the first one -- the conventional coupling constant -- is
responsible for the overall scale while the second constant $\kappa$
parametrizes the strength of a deformation. In two dimensions these sigma
models are perturbatively renormalizable. We calculate their $\beta$ functions
to two loops and find the RG flow of the coupling constants. We calculate the
two-point function in the UV limit, which has a power law dependence with an
exponent dependent on the RG trajectory.
