Reductive homogeneous Lorentzian manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50019326" target="_blank" >RIV/62690094:18470/22:50019326 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0926224522000857?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0926224522000857?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.difgeo.2022.101932" target="_blank" >10.1016/j.difgeo.2022.101932</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Reductive homogeneous Lorentzian manifolds

Popis výsledku v původním jazyce

We study homogeneous Lorentzian manifolds M = G/L of a connected reductive Lie group Gmodulo a connected reductive subgroup L, under the assumption that M is (almost) G-effective and the isotropy representation is totally reducible. We show that the description of such manifolds reduces to the case of semisimple Lie groups G. Moreover, we prove that such a homogeneous space is reductive. We describe all totally reducible subgroups of the Lorentz group and divide them into three types. The subgroups of Type Iare compact, while the subgroups of Type II and Type III are non-compact. The explicit description of the corresponding homogeneous Lorentzian spaces of Type II and III(under some mild assumption) is given. We also show that the description of Lorentz homogeneous manifolds M = G/L of Type I reduces to the description of subgroups L such that M = G/Lis an admissible manifold, i.e., an effective homogeneous manifold that admits an invariant Lorentzian metric. Whenever the subgroup Lis a maximal subgroup with these properties, we call such a manifold minimal admissible. We classify all minimal admissible homogeneous manifolds G/L of a compact semisimple Lie group Ga nd describe all invariant Lorentzian metrics on them. (C) 2022 Elsevier B.V. All rights reserved.

Název v anglickém jazyce

Reductive homogeneous Lorentzian manifolds

Popis výsledku anglicky

We study homogeneous Lorentzian manifolds M = G/L of a connected reductive Lie group Gmodulo a connected reductive subgroup L, under the assumption that M is (almost) G-effective and the isotropy representation is totally reducible. We show that the description of such manifolds reduces to the case of semisimple Lie groups G. Moreover, we prove that such a homogeneous space is reductive. We describe all totally reducible subgroups of the Lorentz group and divide them into three types. The subgroups of Type Iare compact, while the subgroups of Type II and Type III are non-compact. The explicit description of the corresponding homogeneous Lorentzian spaces of Type II and III(under some mild assumption) is given. We also show that the description of Lorentz homogeneous manifolds M = G/L of Type I reduces to the description of subgroups L such that M = G/Lis an admissible manifold, i.e., an effective homogeneous manifold that admits an invariant Lorentzian metric. Whenever the subgroup Lis a maximal subgroup with these properties, we call such a manifold minimal admissible. We classify all minimal admissible homogeneous manifolds G/L of a compact semisimple Lie group Ga nd describe all invariant Lorentzian metrics on them. (C) 2022 Elsevier B.V. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Differential Geometry and its Applications

ISSN

0926-2245

e-ISSN

1872-6984

Svazek periodika

84

Číslo periodika v rámci svazku

October

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

21

Strana od-do

"Article Number: 101932"

Kód UT WoS článku

000838919700001

EID výsledku v databázi Scopus

2-s2.0-85135533295