Thursday, December 20, 2012

1212.4752 (A. C. V. V. de Siqueira)

Conformal Form of Pseudo-Riemannian Metrics by Normal Coordinate
Transformations II

A. C. V. V. de Siqueira
In this paper, we have reintroduced a new approach to conformal geometry developed and presented in two previous papers, in which we show that all n-dimensional pseudo-Riemannian metrics are conformal to a flat n-dimensional manifold as well as an n-dimensional manifold of constant curvature when Riemannian normal coordinates are well-behaved in the origin and in their neighborhood. This was based on an approach developed by French mathematician Elie Cartan. As a consequence of geometry, we have reintroduced the classical and quantum angular momenta of a particle and present new interpretations. We also show that all n-dimensional pseudo-Riemannian metrics can be embedded in a hyper-cone of a flat n+2-dimensional manifold.
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