The Congruence Theorem for Ovaloids

Abstract

Let S and S* be two isometric surfaces (see I, 2.6). Let h be the isometry between S and S* and let u, v be parameters such that X(u,v) and X*(u,v) are corresponding points under the map h . Then S and S* have the same first fundamental forms; i.e.

$$ \left( {{\text{E,F,G}}} \right) = \left( {{\text{E*,F*,G*}}} \right) $$

(1)

.