Conformally Invariant Powers of the Laplacian, <Emphasis Type="Italic">Q</Emphasis>-Curvature,and Tractor Calculus |
| |
Authors: | A Rod Gover Lawrence J Peterson |
| |
Institution: | (1) Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1, New Zealand. E-mail: gover@math.auckland.ac.nz, NZ;(2) Department of Mathematics, The University of North Dakota, Grand Forks, ND 58202-8376, USA. E-mail: lawrence.peterson@und.nodak.edu, US |
| |
Abstract: | We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS
operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian. Conformal tractor
calculus is the natural induced bundle calculus associated to the conformal Cartan connection. Applications discussed include
standard formulae for these operators in terms of the Levi-Civita connection and its curvature and a direct definition and
formula for T. Branson's so-called Q-curvature (which integrates to a global conformal invariant) as well as generalisations of the operators and the Q-curvature. Among examples, the operators of order 4, 6 and 8 and the related Q-curvatures are treated explicitly. The algorithm exploits the ambient metric construction of Fefferman and Graham and includes
a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions. This is
partly based on 12], where the relationship of the normal standard tractor bundle to the ambient construction is described.
Received: 24 January 2002 / Accepted: 1 November 2002 Published online: 18 February 2003
Communicated by P. Sarnak |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|