Conformal holonomy in MacDowell-Mansouri gravity

2014 ◽  
Vol 55 (3) ◽  
pp. 032501 ◽  
Author(s):  
James A. Reid ◽  
Charles H.-T. Wang
Keyword(s):  
Conformal Holonomy

scholarly journals The ambient obstruction tensor and conformal holonomy

2017 ◽  
Vol 290 (2) ◽  
pp. 403-436
Author(s):  
Thomas Leistner ◽  
Andree Lischewski
Keyword(s):  
Conformal Holonomy

scholarly journals Conformal holonomy equals ambient holonomy

2016 ◽  
Vol 285 (2) ◽  
pp. 303-318 ◽  
Author(s):  
Andreas Čap ◽  
A. Gover ◽  
C. Graham ◽  
Matthias Hammerl
Keyword(s):  
Conformal Holonomy

Decomposable conformal holonomy in Riemannian signature

2011 ◽  
Vol 285 (2-3) ◽  
pp. 150-163 ◽  
Author(s):  
Stuart Armstrong ◽  
Felipe Leitner
Keyword(s):  
Conformal Holonomy

scholarly journals A SUB-PRODUCT CONSTRUCTION OF POINCARÉ–EINSTEIN METRICS

2009 ◽  
Vol 20 (10) ◽  
pp. 1263-1287 ◽  
Author(s):  
A. ROD GOVER ◽  
F. LEITNER
Keyword(s):  
Einstein Metrics ◽  
Explicit Construction ◽  
Conformal Structure ◽  
Conformal Class ◽  
Poincaré Metric ◽  
Product Construction ◽  
Einstein Spaces ◽  
Conformal Holonomy ◽  
The Given

Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincaré–Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conformal structure. The ambient metrics have holonomy that agrees with the conformal holonomy. In the generic case the ambient metric arises directly as a product of the metric cones over the original Einstein spaces. In general the conformal infinity of the Poincaré metric we construct is not Einstein, and so this describes a class of non-conformally Einstein metrics for which the (Fefferman–Graham) obstruction tensor vanishes.

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