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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The conformal deformation detour complex for the obstruction tensor


Authors: Thomas P. Branson and A. Rod Gover
Journal: Proc. Amer. Math. Soc. 135 (2007), 2961-2965
MSC (2000): Primary 53A30; Secondary 53A55
Published electronically: May 10, 2007
MathSciNet review: 2317974
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Abstract: On pseudo-Riemannian manifolds of even dimension $ n\geq 4$, with everywhere vanishing (Fefferman-Graham) obstruction tensor, we construct a complex of conformally invariant differential operators. The complex controls the infinitesimal deformations of obstruction-flat structures, and, in the case of Riemannian signature the complex is elliptic.


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Additional Information

Thomas P. Branson
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242

A. Rod Gover
Affiliation: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1, New Zealand
Email: gover@math.auckland.ac.nz

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08932-0
PII: S 0002-9939(07)08932-0
Keywords: conformal differential geometry, elliptic operators
Received by editor(s): June 13, 2006
Published electronically: May 10, 2007
Additional Notes: Both authors would like to thank the Mathematical Sciences Research Institute, Berkeley
The second author would also like to thank the Royal Society of New Zealand for support via Marsden Grant no. 02-UOA-108
Dedicated: The second author dedicates the paper to the memory of Thomas P. Branson (1953–2006)
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2007 American Mathematical Society