  In this earliest study of thick accretion disks with viscosity effects, we
construct stationary solutions of a relativistic geometrically thick accretion
disk in the Schwarzschild spacetime under the influence of shear viscosity and
the curvature of the black hole by solving the general relativistic causal
Navier-Stokes equation. Motivated by the causal prescription of relativistic
hydrodynamics initially introduced in M\"uller-Israel-Stewart theories, our
approach adopts a simplistic path and takes into account of only shear
viscosity, discarding influences of bulk viscosity and heat flow. This work
investigates possible impacts of both the shear viscosity tensor and black hole
curvature on the shape of a thick disk characterized by constant specific
angular momentum distribution. The existence of the integrability condition of
the Navier-Stokes equation has been examined in our study which further
supports the existence of stationary solutions in the given set-up.
