Overcoming diffraction limit is crucial for obtaining high-resolution image
and observing fine microstructure. With this conventional difficulty still
puzzling us and the prosperous development of wave dynamics of light
interacting with gravitational fields in recent years, how spatial curvature
affect the diffraction limit is an attractive and important question. Here we
investigate the issue of diffraction limit and optical resolution on
two-dimensional curved spaces - surfaces of revolution (SORs) with constant or
variable spatial curvature. We show that the diffraction limit decreases and
resolution is improved on SORs with positive Gaussian curvature, opening a new
avenue to super-resolution. The diffraction limit is also influenced by
propagation direction, as well as the propagation distance in curved space with
variable spatial curvature. These results provide a possible method to control
optical resolution in curved space or equivalent waveguides with varying
refractive index distribution and may allow one to detect the presence of
non-uniform strong gravitational effect by probing locally the optical
resolution