Fefferman-Graham ambient metrics of Patterson-Walker metrics
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00101351" target="_blank" >RIV/00216224:14310/18:00101351 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/abs/1608.06875" target="_blank" >https://arxiv.org/abs/1608.06875</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/blms.12136" target="_blank" >10.1112/blms.12136</a>
Alternative languages
Result language
angličtina
Original language name
Fefferman-Graham ambient metrics of Patterson-Walker metrics
Original language description
Given an n-dimensional manifold N with an affine connection D, we show that the associated Patterson-Walker metric g on TN admits a global and explicit Fefferman-Graham ambient metric. This provides a new and large class of conformal structures which are generically not conformally Einstein but for which the ambient metric exists to all orders and can be realised in a natural and explicit way. In particular, it follows that Patterson-Walker metrics have vanishing Fefferman-Graham obstruction tensors. As an application of the concrete ambient metric realisation we show in addition that Patterson-Walker metrics have vanishing Q-curvature. We further show that the relationship between the geometric constructions mentioned above is very close: the explicit Fefferman-Graham ambient metric is itself a Patterson-Walker metric.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
ISSN
0024-6093
e-ISSN
1469-2120
Volume of the periodical
50
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
5
Pages from-to
316-320
UT code for WoS article
000428874300010
EID of the result in the Scopus database
2-s2.0-85044822880