  The stationary hydrodynamic equations for transonic viscous accretion discs
in Kerr geometry are derived. The consistent formulation is given for the
viscous angular momentum transport and the boundary conditions on the horizon
of a central black hole. An expression for the thickness of the disc is
obtained from the vertical Euler equation for general accretion flows with
vanishing vertical velocity. Different solution topologies are identified,
characterized by a sonic transition close to or far from the marginally stable
orbit. A numerical method is presented that allows to integrate the structure
equations of transonic accretion flows. Global polytropic solutions for the
disc structure are calculated, covering each topology and a wide range of
physical conditions. These solutions generally possess a sub-Keplerian angular
momentum distribution and have maximum temperatures in the range
$10^{11}-10^{12}$ K. Accretion discs around rotating black holes are hotter and
deposit less angular momentum on the central object than accretion discs around
Schwarzschild black holes.
