In this paper, we show the existence of real-analytic stationary
Navier-Stokes flows with isotropic streamlines in all latitudes in some
simply-connected flow region on a rotating round sphere. We also exclude the
possibility of having a Poiseuille's flow profile to be one of these stationary
Navier-Stokes flows with isotropic streamlines. When the sphere is replaced by
a 2-dimensional hyperbolic space, we also give the analog existence result for
stationary parallel laminar Navier-Stokes flows along a circular-arc boundary
portion of some compact obstacle in the 2-D hyperbolic space. The existence of
stationary parallel laminar Navier-Stokes flows along a straight boundary of
some obstacle in the 2-D hyperbolic space is also studied. In any one of these
cases, we show that a parallel laminar flow with a Poiseuille's flow profile
ceases to be a stationary Navier-Stokes flow, due to the curvature of the
background manifold
