Francisco J Herranz and Mariano Santander 2002 J. Phys. A: Math. Gen. 35 6619 doi:10.1088/0305-4470/35/31/307
Francisco J Herranz1 and Mariano Santander2
Show affiliationsThe conformal groups for the nine two-dimensional real spaces of constant curvature are realized as matrix groups acting as globally defined linear transformations in a four-dimensional 'conformal ambient space'. This affords a unified and global study of the 'conformal completion' or compactification for the three classical Riemannian spaces as well as of the six relativistic and non-relativistic spacetimes (Minkowskian, de Sitter, anti-de Sitter, both Newton–Hooke and Galilean). The conformal embedding of the initial space into its compactification is carried out explicitly through two methods: either a group-theoretical one involving one-parameter subgroups or a geometric one by means of a stereographic projection. In the Euclidean and Minkowskian spaces the results reduce to the well known ones, but in the generic situation, with any non-zero curvature or arbitrary type signature, the approach is very explicit and provides some new insights.
11.25.Hf Conformal field theory, algebraic structures
02.40.Dr Euclidean and projective geometries
58B20 Riemannian, Finsler and other geometric structures (See also 53C20, 53C60)
Issue 31 (9 August 2002)
Received 2 May 2002
Published 26 July 2002
Francisco J Herranz and Mariano Santander 2002 J. Phys. A: Math. Gen. 35 6619
Wen-bin Fan et al 2006 J. Phys.: Condens. Matter 18 3367
J. S. Lazendic et al. 2006 ApJ 651 250
Gregor Tanner and Niels Søndergaard 2007 J. Phys. A: Math. Theor. 40 R443
Z G Xiao et al 2007 J. Phys. G: Nucl. Part. Phys. 34 S915
M Berrada et al 2009 Inverse Problems 25 115016
A. C. A. Boogert et al. 2004 ApJ 615 344
S Della Longa et al 2009 J. Phys.: Conf. Ser. 190 012202
H Balasin and D Grumiller 2004 Class. Quantum Grav. 21 2859
Stefan Luding 2009 Nonlinearity 22 R101