  We present stationary solutions of magnetized, viscous thick accretion disks
around a Schwarzschild black hole. We assume that the tori are not
self-gravitating, are endowed with a toroidal magnetic field, and obey a
constant angular momentum law. Our study focuses on the role of the black hole
curvature in the shear viscosity tensor and in their potential combined effect
on the stationary solutions. Those are built in the framework of a
causality-preserving, second-order gradient expansion scheme of relativistic
hydrodynamics in the Eckart frame description which gives rise to hyperbolic
equations of motion. The stationary models are constructed by numerically
solving the general relativistic momentum conservation equation using the
method of characteristics. We place constraints in the range of validity of the
second-order transport coefficients of the theory. Our results reveal that the
effects of the shear viscosity and curvature are particularly noticeable only
close to the cusp of the disks. The surfaces of constant pressure are affected
by viscosity and curvature and the self-intersecting isocontour - the cusp -
moves to smaller radii (i.e. towards the black hole horizon) as the effects
become more significant. For highly magnetized disks the shift in the cusp
location is smaller. Our findings might have implications on the dynamical
stability of constant angular momentum tori which, in the inviscid case, are
affected by the runaway instability.
