If q m is positive for all non-zero X m, then the metric is positive-definite at m. If the metric is positive-definite at every m ∈ M, then g is called a Riemannian metric. More generally, if the quadratic forms q m have constant signature independent of m, then the signature of g is this signature, and g is called a pseudo-Riemannian metric. If M is connected, then the signature of q m does not depend on m.