Eikonal equation from Riemanian Length Structure
Given a Riemanian manifold X and a positive scalar velocity field v(X) and the length structure where r(t) is some arbitrary path
then derive the isotropic Eikonal equation for the manifold X and prove that it is equal to
where d(x) is the distance from a source point x0 to x both in X.
and is the length of the minimal geodesic from x0 to x as defined by the riemanian metric and the length structure above.
My problem is that I dont know how to approach this. What constitutes a proof for this?