Representation of a Channel as a Tubular Manifold: Frenet-Serret Moving Frame

In this chapter, we apply the Kalinay-Percus (KP) projection method to narrow channels and tubes where the coordinate frame is placed at the axis curve of the tube or channel, using the Frenet-Serret moving frame as the coordinate system to study the diffusion of bounded Brownian point-like particles. This covariant description for the diffusion equation maps the shape of a general channel in two dimensions or a tube in three dimensions, in a straight tube or channel seen in a non-Cartesian space.