Homogeneous Einstein metrics on non-Kahler C-spaces

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Homogeneous Einstein metrics on non-Kahler C-spaces

Popis výsledku v původním jazyce

We study homogeneous Einstein metrics on indecomposable non-Kahler C-spaces, i.e. even-dimensional torus bundles M = G/H with rank G &gt; 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.

Název v anglickém jazyce

Homogeneous Einstein metrics on non-Kahler C-spaces

Popis výsledku anglicky

We study homogeneous Einstein metrics on indecomposable non-Kahler C-spaces, i.e. even-dimensional torus bundles M = G/H with rank G &gt; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-14466Y" target="_blank" >GJ19-14466Y: Speciální metriky v supergravitaci a nové G-struktury</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Journal of geometry and physics

ISSN

0393-0440

e-ISSN

—

Svazek periodika

160

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

31

Strana od-do

"Article Number: 103996"

Kód UT WoS článku

000623891500006

EID výsledku v databázi Scopus

2-s2.0-85096197348