Brownian self-driven particles on Riemannian surfaces

We present the dynamics of overdamped Brownian self-propelled particles (swimmers) moving on a general Riemannian surface. In particular, we offer analytical results (mean-square displacement and variance) to characterize the effect of self-propulsion and geometry on the diffusion of swimmers moving on prolate and oblate spheroids. Our results are compared with Brownian dynamics simulations and an excellent agreement is obtained. Marginal probability density functions are also obtained.