Principal Mappings of 3-dimensional Riemannian Spaces into Spaces of Constant Curvature

Details Principal Mappings of 3-dimensional Riemannian Spaces into Spaces of Constant Curvature Principal Mappings of 3-dimensional Riemannian Spaces into Spaces of Constant Curvature

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996gregr..28.1139b&link_type=abstract

General Relativity and Gravitation, Volume 28, Issue 9, pp.1139-1150

Physics

9

Scientific paper

As is well-known, the Gauss theorem, according to which any 2-dimensional Riemannian metric can be mapped locally conformally into an euclidean space, does not hold in three dimensions. We define in this paper transformations of a new type, that we call principal. They map 3-dimensional spaces into spaces of constant curvature. We give a few explicit examples of principal transformations and we prove, at the linear approximation, that any metric deviating not too much from the euclidean metric can be mapped by a principal transformation into the euclidean metric.

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