| HAMMERL, Matthias, Katja SAGERSCHNIG, Josef ŠILHAN, Arman TAGHAVI-CHABERT and Vojtěch ŽÁDNÍK. Fefferman-Graham ambient metrics of Patterson-Walker metrics. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. HOBOKEN: WILEY, 2018, vol. 50, No 2, p. 316-320. ISSN 0024-6093. Available from: https://dx.doi.org/10.1112/blms.12136. |
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@article{1469261,
author = {Hammerl, Matthias and Sagerschnig, Katja and Šilhan, Josef and TaghaviandChabert, Arman and Žádník, Vojtěch},
article_location = {HOBOKEN},
article_number = {2},
doi = {http://dx.doi.org/10.1112/blms.12136},
keywords = {projective structure; conformal structure; ambient metric},
language = {eng},
issn = {0024-6093},
journal = {BULLETIN OF THE LONDON MATHEMATICAL SOCIETY},
title = {Fefferman-Graham ambient metrics of Patterson-Walker metrics},
url = {https://arxiv.org/abs/1608.06875},
volume = {50},
year = {2018}
}
TY - JOUR
ID - 1469261
AU - Hammerl, Matthias - Sagerschnig, Katja - Šilhan, Josef - Taghavi-Chabert, Arman - Žádník, Vojtěch
PY - 2018
TI - Fefferman-Graham ambient metrics of Patterson-Walker metrics
JF - BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
VL - 50
IS - 2
SP - 316-320
EP - 316-320
PB - WILEY
SN - 00246093
KW - projective structure
KW - conformal structure
KW - ambient metric
UR - https://arxiv.org/abs/1608.06875
L2 - https://arxiv.org/abs/1608.06875
N2 - 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.
ER -
HAMMERL, Matthias, Katja SAGERSCHNIG, Josef ŠILHAN, Arman TAGHAVI-CHABERT and Vojtěch ŽÁDNÍK. Fefferman-Graham ambient metrics of Patterson-Walker metrics. \textit{BULLETIN OF THE LONDON MATHEMATICAL SOCIETY}. HOBOKEN: WILEY, 2018, vol.~50, No~2, p.~316-320. ISSN~0024-6093. Available from: https://dx.doi.org/10.1112/blms.12136.
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