Fefferman-Graham ambient metrics of Patterson-Walker metrics

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Fefferman-Graham ambient metrics of Patterson-Walker metrics

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Fefferman-Graham ambient metrics of Patterson-Walker metrics

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY

ISSN

0024-6093

e-ISSN

1469-2120

Svazek periodika

50

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

5

Strana od-do

316-320

Kód UT WoS článku

000428874300010

EID výsledku v databázi Scopus

2-s2.0-85044822880