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arXiv · 1006.2868

Conformal Form of Pseudo-Riemannian Metrics by Normal Coordinate Transformations

A. C. V. V. de Siqueira
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Abstract

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.

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A. C. V. V. de Siqueira. 2010-06-15. Conformal Form of Pseudo-Riemannian Metrics by Normal Coordinate Transformations. https://arxiv.org/abs/1006.2868

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