Skew-product decomposition of Brownian motion on an ellipsoid

In this article we obtain a skew-product decomposition of a Brownian motion on an ellipsoid of dimension in a Euclidean space of dimension. We only consider such ellipsoid whose restriction to first dimensions is a sphere and its last coordinate depends on a variable parameter. We prove that the projection of this Brownian motion on to the last coordinate is, after a suitable transformation, a Wright–Fisher diffusion process with atypical selection coefficient