Ikeda-Watanabe's connection and Navier-Stokes equations

Abstract：To each velocity, we associate an affine connection introduced by N. Ikeda and S. Watanabe when they rolled a flat Brownian motion on manifolds. We will compute the associated intrinsic Ricci tensor in the sense of B. Driver, which will allow us to express the vorticity form of Navier-Stokes equations: this can be seen as a non linear version of Bochner-Weitzenbock formula.