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VOL. 14 | 2013 Conformal Form of Pseudo-Riemannian Metrics by Normal Coordinate Transformations II
Antonio de Siqueira

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

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.

Information

Published: 1 January 2013
First available in Project Euclid: 13 July 2015

zbMATH: 1382.53006
MathSciNet: MR3183939

Digital Object Identifier: 10.7546/giq-14-2013-176-200

Rights: Copyright © 2013 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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