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The Ambient Metric (AM-178)$
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Charles Fefferman and C. Robin Graham

Print publication date: 2011

Print ISBN-13: 9780691153131

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153131.001.0001

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Conformai Curvature Tensors

Conformai Curvature Tensors

Chapter:
(p.56) Chapter Six Conformai Curvature Tensors
Source:
The Ambient Metric (AM-178)
Author(s):

Charles Fefferman

C. Robin Graham

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153131.003.0006

This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to g. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group O(p + 1, q + 1) on tensors. It is assumed throughout this chapter that n ≥ 3.

Keywords:   conformal curvature tensors, pseudo-Riemannian metric, conformal geometry, ambient metric

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