  In this paper we extend the Cartan's approach of Riemannian normal
coordinates and show that all n-dimensional pseudo-Riemannian metrics are
conformal to a flat manifold, when, in normal coordinates, they are
well-behaved in the origin and in its neighborhood. We show that for this
condition all n-dimensioanl pseudo-Riemannian metrics can be embedded in a
hyper-cone of an n+2-dimensional flat manifold. Based on the above conditions
we show that each n-dimensional pseudo-Riemannian manifolds is conformal to an
n-dimensional manifold of constant curvature. As a consequence of geometry,
without postulates, we obtain the classical and the quantum angular momenta of
a particle.
