In this paper, we have reintroduced a new approach to conformal geometrydeveloped and presented in two previous papers, in which we show that alln-dimensional pseudo-Riemannian metrics are conformal to a flat n-dimensionalmanifold as well as an n-dimensional manifold of constant curvature whenRiemannian normal coordinates are well-behaved in the origin and in theirneighborhood. This was based on an approach developed by French mathematicianElie Cartan. As a consequence of geometry, we have reintroduced the classicaland quantum angular momenta of a particle and present new interpretations. Wealso show that all n-dimensional pseudo-Riemannian metrics can be embedded in ahyper-cone of a flat n+2-dimensional manifold.
展开▼
