A four-dimensional manifold has coordinates (u, v, w, p) in which the metric has components guv = gww = gpp = 1, all other independent components vanishing.
(a) Show that the manifold is flat and the signature is + 2.
(b) The result in (a) implies the manifold must be Minkowski spacetime. Find a coordinate transformation to the usual coordinates (t, x, y, z). (You may find it a useful hint to calculate ν · ν and u · u.)