  We consider reaction-diffusion equations on a thick curved surface and obtain
a set of effective R-D equation to ${\cal O}(\epsilon^2)$, where $\epsilon$ is
the surface thickness. We observe that the R-D systems on these curved surfaces
can have space- dependent reaction kinetics. Further, we use linear stability
analysis to study the Schnakenberg model on spherical and cylindrical
geometries. The dependence of steady state on the thickness is determined for
both cases, and we find that a change in the thickness can stabilize the
unstable patterns, and vice versa. The combined effect of thickness and
curvature can play an important role in the rearrangement of spatial patterns
on thick curved surfaces.
