Apparently, a divergence free unit normal to a regular parameterized surface sitting in 3 dimensional Euclidian space implies the Gauss Map is divergence free (zero change in flow of the vector field with respect to the integrated flow of the surface area traced out by the unit normal to the surface and of the Gauss Map, and so the surface is minimal).
Does the same result carry over to an n-1 dimensional Gauss Map? That is, does a divergence free n-1 dimensional Gauss Map imply an n-1 dimensional minimal submanifold? If so, can you give me any insight why?