Fefferman-Graham ambient metrics of Patterson-Walker metrics

J 2018

Fefferman-Graham ambient metrics of Patterson-Walker metrics

HAMMERL, Matthias; Katja SAGERSCHNIG; Josef ŠILHAN; Arman TAGHAVI-CHABERT; Vojtěch ŽÁDNÍK et al.

Základní údaje

Originální název

Fefferman-Graham ambient metrics of Patterson-Walker metrics

Autoři

HAMMERL, Matthias; Katja SAGERSCHNIG; Josef ŠILHAN; Arman TAGHAVI-CHABERT a Vojtěch ŽÁDNÍK

Vydání

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, HOBOKEN, WILEY, 2018, 0024-6093

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.767

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/18:00101351

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1112/blms.12136

UT WoS

000428874300010

EID Scopus

2-s2.0-85044822880

Klíčová slova anglicky

projective structure; conformal structure; ambient metric

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 7. 3. 2019 21:23, doc. Mgr. Vojtěch Žádník, Ph.D.

Anotace

V originále

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.

Návaznosti

GBP201/12/G028, projekt VaV

Název: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Investor: Grantová agentura ČR, Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Citovat

HAMMERL, Matthias; Katja SAGERSCHNIG; Josef ŠILHAN; Arman TAGHAVI-CHABERT a Vojtěch ŽÁDNÍK. Fefferman-Graham ambient metrics of Patterson-Walker metrics. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. HOBOKEN: WILEY, 2018, roč. 50, č. 2, s. 316-320. ISSN 0024-6093. Dostupné z: https://doi.org/10.1112/blms.12136.

@article{1469261,
   author = {Hammerl, Matthias and Sagerschnig, Katja and Šilhan, Josef and TaghaviandChabert, Arman and Žádník, Vojtěch},
   article_location = {HOBOKEN},
   article_number = {2},
   doi = {https://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 a Vojtěch ŽÁDNÍK. Fefferman-Graham ambient metrics of Patterson-Walker metrics. \textit{BULLETIN OF THE LONDON MATHEMATICAL SOCIETY}. HOBOKEN: WILEY, 2018, roč.~50, č.~2, s.~316-320. ISSN~0024-6093. Dostupné z: https://doi.org/10.1112/blms.12136.

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