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. #m/def/geo/diff

#state/tidy | #lang/en | #SemBr