Semi-Riemannian manifold Signature of a semi-Riemannian manifold Let be a Semi-Riemannian manifold. At any point, is congruent to a matrix of the form where by Sylvester’s law of inertia the quantity is uniquely determined continuous function of points on the manifold. Thus if is connected, we have a uniquely determined signature for the entire manifold. diff tidy | en | sembr