SPECT is primarily used in the clinic for cardiac myocardial perfusion imaging. However, for SPECT, sensitivity is impaired due to the need for collimation. System resolution FWHM is poor as well (~ 1 cm). In this work the resolution of a curved detector was theoretically derived. The advantage of a curved detector over a flat detector with pinhole collimation was demonstrated for cardiac applications using theoretical derivations as well as a ray-tracing voxel-based forward projector. For the flat detector using parameters close to what was expected for the new multi-pinhole GE Discovery system, it is shown that using a paraboloid detector one may obtain a better system resolution (about 29% better on the average), keeping same pinhole opening. Alternately, sensitivity gains of as much as 2.25 may be obtained, for similar resolutions as a flat detector by just using a different pinhole with higher hole-diameter.