  We present analytic solutions of Maxwell equations in the internal and
external background spacetime of a slowly rotating magnetized neutron star. The
star is considered isolated and in vacuum, with a dipolar magnetic field not
aligned with the axis of rotation. With respect to a flat spacetime solution,
general relativity introduces corrections related both to the monopolar and the
dipolar parts of the gravitational field. In particular, we show that in the
case of infinite electrical conductivity general relativistic corrections due
to the dragging of reference frames are present, but only in the expression for
the electric field. In the case of finite electrical conductivity, however,
corrections due both to the spacetime curvature and to the dragging of
reference frames are shown to be present in the induction equation. These
corrections could be relevant for the evolution of the magnetic fields of
pulsars and magnetars. The solutions found, while obtained through some
simplifying assumption, reflect a rather general physical configuration and
could therefore be used in a variety of astrophysical situations.
