Homogeneous Einstein metrics on non-Kahler C-spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50018574" target="_blank" >RIV/62690094:18470/21:50018574 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0393044020302552?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0393044020302552?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.geomphys.2020.103996" target="_blank" >10.1016/j.geomphys.2020.103996</a>
Alternative languages
Result language
angličtina
Original language name
Homogeneous Einstein metrics on non-Kahler C-spaces
Original language description
We study homogeneous Einstein metrics on indecomposable non-Kahler C-spaces, i.e. even-dimensional torus bundles M = G/H with rank G > rank H over flag manifolds F = G/K of a compact simple Lie group G. Based on the theory of painted Dynkin diagrams we present the classification of such spaces. Next we focus on the family M-l,M-m,M-n := SU(l + m + n)/SU(l) x SU(m) x SU(n) , l, m, n is an element of Z(+) and examine several of its geometric properties. We show that invariant metrics on M-l,M-m,M-n are not diagonal and beyond certain exceptions their parametrization depends on six real parameters. By using such an invariant Riemannian metric, we compute the diagonal and the non-diagonal part of the Ricci tensor and present explicitly the algebraic system of the homogeneous Einstein equation. For general positive integers l, m, n, by applying mapping degree theory we provide the existence of at least one SU(l + m + n)-invariant Einstein metric on M-l,M-m,M-n. For l = m we show the existence of two SU(2m + n)-invariant Einstein metrics on M-m,M-m,M-n, and for l = m = n we obtain four SU(3n)-invariant Einstein metrics on M-n,M-n,M-n. We also examine the isometry problem for these metrics, while for a plethora of cases induced by fixed l, m, n, we provide the numerical form of all non-isometric invariant Einstein metrics. (C) 2020 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
<a href="/en/project/GJ19-14466Y" target="_blank" >GJ19-14466Y: Special metrics in supergravity and new G-structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of geometry and physics
ISSN
0393-0440
e-ISSN
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Volume of the periodical
160
Issue of the periodical within the volume
February
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
31
Pages from-to
"Article Number: 103996"
UT code for WoS article
000623891500006
EID of the result in the Scopus database
2-s2.0-85096197348