 Equivalently, for all vectors "U", "V" at "p", II("U", "V") = "g""p"("U", "V")formula_20, where formula_20 is the mean curvature vector at "p".A submanifold is said to be umbilic (or all-umbilic) if this condition holds at every point "p".This is equivalent to saying that the submanifold can be made totally geodesic by an appropriate conformal change of the metric of the surrounding ("ambient") manifold.