The gap phenomenon for conformally related Einstein metrics

J 2024

The gap phenomenon for conformally related Einstein metrics

ŠILHAN, Josef a Jan GREGOROVIČ

Základní údaje

Originální název

The gap phenomenon for conformally related Einstein metrics

Autoři

ŠILHAN, Josef a Jan GREGOROVIČ

Vydání

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, HOBOKEN, WILEY, 2024, 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: 0.900

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/24:00139604

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Einstein metric; conformal geometry; submaximal dimension; normal conformal Killing fields

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 31. 1. 2025 14:31, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

We determine the submaximal dimensions of the spaces of almost Einstein scales and normal conformal Killing fields for connected conformal manifolds. The results depend on the signature and dimension n of the conformally nonflat conformal manifold. In definite signature, these two dimensions are at most n-3 and (n-4)(n-3)/2, respectively. In Lorentzian signature, these two dimensions are at most n-2 and (n-3)(n-2)/2, respectively. In the remaining signatures, these two dimensions are at most n-1 and (n-2)(n-1)/2, respectively. This upper bound is sharp and to realize examples of submaximal dimensions, we first provide them directly in dimension 4. In higher dimensions, we construct the submaximal examples as the (warped) product of the (pseudo)-Euclidean base of dimension n-4 with one of the 4-dimensional submaximal examples.

Návaznosti

GX19-28628X, projekt VaV

Název: Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou

Investor: Grantová agentura ČR, Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou

Citovat

ŠILHAN, Josef a Jan GREGOROVIČ. The gap phenomenon for conformally related Einstein metrics. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. HOBOKEN: WILEY, 2024, roč. 56, č. 10, s. 3209-3228. ISSN 0024-6093. Dostupné z: https://doi.org/10.1112/blms.13128.

@article{2453739,
   author = {Šilhan, Josef and Gregorovič, Jan},
   article_location = {HOBOKEN},
   article_number = {10},
   doi = {https://doi.org/10.1112/blms.13128},
   keywords = {Einstein metric; conformal geometry; submaximal dimension; normal conformal Killing fields},
   language = {eng},
   issn = {0024-6093},
   journal = {BULLETIN OF THE LONDON MATHEMATICAL SOCIETY},
   title = {The gap phenomenon for conformally related Einstein metrics},
   url = {https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/blms.13128},
   volume = {56},
   year = {2024}
}

TY  - JOUR
ID  - 2453739
AU  - Šilhan, Josef - Gregorovič, Jan
PY  - 2024
TI  - The gap phenomenon for conformally related Einstein metrics
JF  - BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
VL  - 56
IS  - 10
SP  - 3209-3228
EP  - 3209-3228
PB  - WILEY
SN  - 00246093
KW  - Einstein metric
KW  - conformal geometry
KW  - submaximal dimension
KW  - normal conformal Killing fields
UR  - https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/blms.13128
N2  - We determine the submaximal dimensions of the spaces of almost Einstein scales and normal conformal Killing fields for connected conformal manifolds. The results depend on the signature and dimension n of the conformally nonflat conformal manifold. In definite signature, these two dimensions are at most n-3 and (n-4)(n-3)/2, respectively. In Lorentzian signature, these two dimensions are at most n-2 and (n-3)(n-2)/2, respectively. In the remaining signatures, these two dimensions are at most n-1 and (n-2)(n-1)/2, respectively. This upper bound is sharp and to realize examples of submaximal dimensions, we first provide them directly in dimension 4. In higher dimensions, we construct the submaximal examples as the (warped) product of the (pseudo)-Euclidean base of dimension n-4 with one of the 4-dimensional submaximal examples.
ER  -

ŠILHAN, Josef a Jan GREGOROVIČ. The gap phenomenon for conformally related Einstein metrics. \textit{BULLETIN OF THE LONDON MATHEMATICAL SOCIETY}. HOBOKEN: WILEY, 2024, roč.~56, č.~10, s.~3209-3228. ISSN~0024-6093. Dostupné z: https://doi.org/10.1112/blms.13128.

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