  We analyze a broad class of stationary solutions with residual N=1
supersymmetry of four-dimensional N=2 supergravity theories with terms
quadratic in the Weyl tensor. These terms are encoded in a holomorphic
function, which determines the most relevant part of the action and which plays
a central role in our analysis. The solutions include extremal black holes and
rotating field configurations, and may have multiple centers. We prove that
they are expressed in terms of harmonic functions associated with the electric
and magnetic charges carried by the solutions by a proper generalization of the
so-called stabilization equations. Electric/magnetic duality is manifest
throughout the analysis.
  We also prove that spacetimes with unbroken supersymmetry are fully
determined by electric and magnetic charges. This result establishes the
so-called fixed-point behavior according to which the moduli fields must flow
towards certain prescribed values on a fully supersymmetric horizon, but now in
a more general context with higher-order curvature interactions. We briefly
comment on the implications of our results for the metric on the moduli space
of extremal black hole solutions.
