Conformal Form of Pseudo-Riemannian Metrics by Normal Coordinate Transformations II
Abstract
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.
Keywords
Cite
@article{arxiv.1212.4752,
title = {Conformal Form of Pseudo-Riemannian Metrics by Normal Coordinate Transformations II},
author = {A. C. V. V. de Siqueira},
journal= {arXiv preprint arXiv:1212.4752},
year = {2012}
}
Comments
33 pages,no figures. Paper of a talk given at the 14th International Conference on Geometry, Integrability and Quantization (Varna, Bulgaria, June 2012)