Reductive homogeneous Lorentzian manifolds
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Reductive homogeneous Lorentzian manifolds
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Differential Geometry and its Applications
ISSN
0926-2245
e-ISSN
1872-6984
Volume of the periodical
84
Issue of the periodical within the volume
October
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
21
Pages from-to
"Article Number: 101932"
UT code for WoS article
000838919700001
EID of the result in the Scopus database
2-s2.0-85135533295