  Rotating spiral waves organize spatial patterns in chemical, physical and
biological excitable systems. Factors affecting their dynamics such as
spatiotemporal drift are of great interest for par- ticular applications. Here,
we propose a quantitative description for spiral wave dynamics on curved
surfaces which shows that for a wide class of systems, including the BZ
reaction and anisotropic cardiac tissue, the Ricci curvature scalar of the
surface is the main determinant of spiral wave drift. The theory provides
explicit equations for spiral wave drift direction, drift velocity and the
period of rotation. Depending on the parameters, the drift can be directed to
the regions of either maximal or minimal Ricci scalar curvature, which was
verified by direct numerical simulations.
