Umbilic point
Template:Point property in riemannian manifold
Definition
A point in a Riemannian manifold is said to be an umbilic point if the curvature of the shape operator at that point is the same in every direction. In particular, in the case of a surfac, a point is said to be an umbilic point if the principal curvatures are equal, and hence the curvature is the same in all directions.