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https://hdl.handle.net/2440/124001
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Type: | Journal article |
Title: | Explicit ambient metrics and holonomy |
Author: | Anderson, I.M. Leistner, T. Nurowski, P. |
Citation: | Journal of Differential Geometry, 2020; 114(2):193-242 |
Publisher: | International Press |
Issue Date: | 2020 |
ISSN: | 1945-743X 1945-743X |
Statement of Responsibility: | Ian M. Anderson, Thomas Leistner and Paweł Nurowski |
Abstract: | We present three large classes of examples of conformal structures whose Fefferman–Graham ambient metrics can be found explicitly. Our method for constructing these examples rests upon a set of sufficiency conditions under which the Fefferman–Graham equations are assured to reduce to a system of inhomogeneous linear partial differential equations. Our examples include conformal pp-waves and, more importantly, conformal structures that are defined by generic co-rank 3 distributions in dimensions 5 and 6. Our examples illustrate various aspects of the ambient metric construction. The holonomy algebras of our ambient metrics are studied in detail. In particular, we exhibit a large class of metrics with holonomy equal to the exceptional non-compact Lie group G2 as well as ambient metrics with holonomy contained in Spin(4,3). |
Keywords: | math.DG Primary: 53C29, 53A30, secondary: 53C50 |
Rights: | Copyright status unknown |
DOI: | 10.4310/jdg/1580526015 |
Grant ID: | http://purl.org/au-research/grants/arc/DP120104582 http://purl.org/au-research/grants/arc/FT110100429 |
Published version: | https://projecteuclid.org/euclid.jdg/1580526015 |
Appears in Collections: | Aurora harvest 4 Mathematical Sciences publications |
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