A strong pseudo-Riemannian metric on a smooth manifold M is a (0, 2) tensor field g which is symmetric and for which, at each m element M, the map v_m ↦g_m(v_m, ·) is an isomorphism of T_m M onto T_m^* M. This latter condition is called strong non-degeneracy.

Lorentzian manifold | metric signature | metric tensor | metric tensor index | positive definite tensor | pseudo-Euclidean space | pseudo-Riemannian manifold | semi-Riemannian manifold | semi-Riemannian metric | smooth manifold | strong Riemannian metric | weak pseudo-Riemannian metric | weak Riemannian metric

Bernhard Riemann