A Projective-to-Conformal Fefferman-Type Construction

J 2017

A Projective-to-Conformal Fefferman-Type Construction

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

Základní údaje

Originální název

A Projective-to-Conformal Fefferman-Type Construction

Autoři

HAMMERL, Matthias (40 Rakousko), Katja SAGERSCHNIG (40 Rakousko), Josef ŠILHAN (203 Česká republika, domácí), Arman TAGHAVI-CHABERT (250 Francie, domácí) a Vojtěch ŽÁDNÍK (203 Česká republika, domácí)

Vydání

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 2017, 1815-0659

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Ukrajina

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.100

Kód RIV

RIV/00216224:14310/17:00095269

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.3842/SIGMA.2017.081

UT WoS

000414168700001

Klíčová slova anglicky

parabolic geometry; projective structure; conformal structure; Cartan connection; Fefferman spaces; twistor spinors

Štítky

NZ, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 27. 3. 2018 16:45, Ing. Nicole Zrilić

Anotace

V originále

We study a Fefferman-type construction based on the inclusion of Lie groups SL(n + 1) into Spin(n + 1, n + 1). The construction associates a split-signature (n, n)-conformal spin structure to a projective structure of dimension n. We prove the existence of a canonical pure twistor spinor and a light-like conformal Killing field on the constructed conformal space. We obtain a complete characterisation of the constructed conformal spaces in terms of these solutions to overdetermined equations and an integrability condition on the Weyl curvature. The Fefferman-type construction presented here can be understood as an alternative approach to study a conformal version of classical Patterson-Walker metrics as discussed in recent works by Dunajski-Tod and by the authors. The present work therefore gives a complete exposition of conformal Patterson-Walker metrics from the viewpoint of parabolic geometry.

Návaznosti

GA201/08/0397, projekt VaV

Název: Algebraické metody v geometrii a topologii

Investor: Grantová agentura ČR, Algebraické metody v geometrii a topologii

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

GP14-27885P, projekt VaV

Název: Skoro izotropní struktury v pseudo-riemannovské geometrii

Investor: Grantová agentura ČR, Skoro izotropní struktury v pseudo-riemannovské geometrii

Citovat

HAMMERL, Matthias, Katja SAGERSCHNIG, Josef ŠILHAN, Arman TAGHAVI-CHABERT a Vojtěch ŽÁDNÍK. A Projective-to-Conformal Fefferman-Type Construction. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2017, roč. 13, č. 81, s. 1-33. ISSN 1815-0659. Dostupné z: https://dx.doi.org/10.3842/SIGMA.2017.081.

@article{1399439,
   author = {Hammerl, Matthias and Sagerschnig, Katja and Šilhan, Josef and TaghaviandChabert, Arman and Žádník, Vojtěch},
   article_number = {81},
   doi = {http://dx.doi.org/10.3842/SIGMA.2017.081},
   keywords = {parabolic geometry; projective structure; conformal structure; Cartan connection; Fefferman spaces; twistor spinors},
   language = {eng},
   issn = {1815-0659},
   journal = {Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)},
   title = {A Projective-to-Conformal Fefferman-Type Construction},
   url = {https://www.emis.de/journals/SIGMA/2017/081/},
   volume = {13},
   year = {2017}
}

TY  - JOUR
ID  - 1399439
AU  - Hammerl, Matthias - Sagerschnig, Katja - Šilhan, Josef - Taghavi-Chabert, Arman - Žádník, Vojtěch
PY  - 2017
TI  - A Projective-to-Conformal Fefferman-Type Construction
JF  - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
VL  - 13
IS  - 81
SP  - 1-33
EP  - 1-33
SN  - 18150659
KW  - parabolic geometry
KW  - projective structure
KW  - conformal structure
KW  - Cartan connection
KW  - Fefferman spaces
KW  - twistor spinors
UR  - https://www.emis.de/journals/SIGMA/2017/081/
L2  - https://www.emis.de/journals/SIGMA/2017/081/
N2  - We study a Fefferman-type construction based on the inclusion of Lie groups SL(n + 1) into Spin(n + 1, n + 1). The construction associates a split-signature (n, n)-conformal spin structure to a projective structure of dimension n. We prove the existence of a canonical pure twistor spinor and a light-like conformal Killing field on the constructed conformal space. We obtain a complete characterisation of the constructed conformal spaces in terms of these solutions to overdetermined equations and an integrability condition on the Weyl curvature. The Fefferman-type construction presented here can be understood as an alternative approach to study a conformal version of classical Patterson-Walker metrics as discussed in recent works by Dunajski-Tod and by the authors. The present work therefore gives a complete exposition of conformal Patterson-Walker metrics from the viewpoint of parabolic geometry.
ER  -

HAMMERL, Matthias, Katja SAGERSCHNIG, Josef ŠILHAN, Arman TAGHAVI-CHABERT a Vojtěch ŽÁDNÍK. A Projective-to-Conformal Fefferman-Type Construction. \textit{Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)}. 2017, roč.~13, č.~81, s.~1-33. ISSN~1815-0659. Dostupné z: https://dx.doi.org/10.3842/SIGMA.2017.081.

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