  (abbreviated) In this paper we derive equations describing dynamics and
stationary configurations of a twisted fully relativistic thin accretion disc
around a slowly rotating black hole. We find that the disc dynamics and
stationary shapes are determined by a pair of equations for two complex
variables describing orientation of the disc rings and velocity perturbations
in the disc. We analyse shapes of stationary twisted configurations. It is
shown that the stationary configurations depend on two parameters - the $\alpha
$parameter and $\tilde \delta = \delta_{*}/\sqrt a$, where $\delta_{*}\sim h/r$
is the disc opening angle (h is the disc halfthickness) and $a$ is the black
hole rotational parameter. When $a > 0$ and $\tilde \delta \ll 1$ the shapes
depend drastically on value of $\alpha$. When $\alpha $ is small the disc
inclination angle oscillates with radius with amplitude and radial frequency of
the oscillations dramatically increasing towards the last stable orbit. For
moderate values of $\alpha $ the oscillations do not take place but the disc
does not align with the equatorial plane at small radii. Its inclination angle
is either increasing towards $R_{ms}$ or exhibits a non-monotonic dependence on
the radial coordinate. Finally, when $\alpha $ is sufficiently large the disc
aligns with the equatorial plane at small radii. When $a < 0$ the disc aligns
with the equatorial plane for all values of $\alpha $. The results reported
here may have implications for determining structure and variability of
accretion discs close to $R_{ms}$ as well as for modelling of emission spectra
coming from different sources, which are supposed to contain black holes.
