In a general metric space of four dimensions, with an interval given by , where – ds2 = gμνdxμdxν, where g = ║gμν║<0, we can choose locally galilean coordinates at any point. The initial directions of the axes can be fixed in an absolute fashion as the directions of the principal axes of the quadric Gμνdxμdxν = const., is the contracted Riemann-Christoffel tensor.