Francisco J Herranz and Mariano Santander 2002 J. Phys. A: Math. Gen. 35 6601 doi:10.1088/0305-4470/35/31/306
Francisco J Herranz1 and Mariano Santander2
Show affiliationsIn this paper, we give a unified and global new approach to the study of the conformal structure of the three classical Riemannian spaces as well as of the six relativistic and non-relativistic spacetimes (Minkowskian, de Sitter, anti-de Sitter, and both Newton–Hooke and Galilean). We obtain general expressions within a Cayley–Klein framework, holding simultaneously for all these nine spaces, whose cycles (including geodesics and circles) are explicitly characterized in a new way. The corresponding cycle-preserving symmetries, which give rise to (Möbius-like) conformal Lie algebras, together with their differential realizations are then deduced without having to resort to solving the conformal Killing equations. We show that each set of three spaces with the same signature type and any curvature have isomorphic conformal algebras; these are related through an apparently new conformal duality. Laplace and wave-type differential equations with conformal algebra symmetry are finally constructed.
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
81T40 Two-dimensional field theories, conformal field theories, etc.
Issue 31 (9 August 2002)
Received 30 November 2001, in final form 2 May 2002
Published 26 July 2002
Francisco J Herranz and Mariano Santander 2002 J. Phys. A: Math. Gen. 35 6601
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