Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F13%3A00067051" target="_blank" >RIV/00216224:14310/13:00067051 - isvavai.cz</a>

Result on the web

<a href="http://www.worldscientific.com/doi/abs/10.1142/S0129167X13500778?af=R" target="_blank" >http://www.worldscientific.com/doi/abs/10.1142/S0129167X13500778?af=R</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0129167X13500778" target="_blank" >10.1142/S0129167X13500778</a>

Result language

angličtina

Original language name

Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands

Original language description

We construct the homogeneous Einstein equation for generalized flag manifolds G/K of a compact simple Lie group G whose isotropy representation decomposes into five inequivalent irreducible Ad(K)-submodules. To this end, we apply a new technique which isbased on a fibration of a flag manifold over another such space and the theory of Riemannian submersions.We classify all generalized flag manifolds with five isotropy summands, and we use Grobner bases to study the corresponding polynomial systems for the Einstein equation. For the generalized flag manifolds E6 /(SU(4)xSU(2)xU(1) x U(1)) and E7 /(U(1)xU(6)) we find explicitly all invariant Einstein metrics up to isometry. For the generalized flag manifolds SO(2n +1)/(U(1) xU(p)xSO(2(n-p-1)+ 1)) and SO(2n)/(U(1)xU(p)xSO(2(n-p-1))) we prove existence of at least two non-Kahler Einstein metrics. For small values of n and p we give the precise number of invariant Einstein metrics.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>

Continuities

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

Publication year

2013

Confidentiality

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

Name of the periodical

International Journal of Mathematics

ISSN

0129-167X

e-ISSN

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Volume of the periodical

24

Issue of the periodical within the volume

10

Country of publishing house

SG - SINGAPORE

Number of pages

52

Pages from-to

1-52

UT code for WoS article

000326463200001

EID of the result in the Scopus database

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