Brownian Motion On K(a|")Hler Manifold

Kahler manifold has more complicated structures than Riemannian manifold. Therefore Brownian Motion on Kahler manifold must have some special properties. Since Brown Motion on Riemannian manifold can be constructed by stochastic dif-ferential equations we can obtain Brownian Motion on Kahler Manifold in a similar way. The Brownian motion on a Kahler manifold M is the diffusion process on M generated by the differential operator given by the Laplace-Beltrami operator on M. Therefore it is very important to find out what is the Laplace-Beltrami operator on M.