Homogeneous Einstein metrics on generalized flag manifolds with
five isotropy summands

J 2013

Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands

CHRYSIKOS, Ioannis; Andreas ARVANITOYEORGOS a Yusuke SAKANE

Základní údaje

Originální název

Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands

Autoři

CHRYSIKOS, Ioannis; Andreas ARVANITOYEORGOS a Yusuke SAKANE

Vydání

International Journal of Mathematics, 2013, 0129-167X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Singapur

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.552

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/13:00067051

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1142/S0129167X13500778

UT WoS

000326463200001

Klíčová slova anglicky

Homogeneous space; Einstein metric; Riemannian submersion; generalized flag manifold; isotropy representation; Weyl group.

Štítky

AKR, rivok

Změněno: 29. 4. 2014 16:11, Ing. Andrea Mikešková

Anotace

V originále

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 is based 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.

Návaznosti

GBP201/12/G028, projekt VaV

Název: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Investor: Grantová agentura ČR, Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Citovat

CHRYSIKOS, Ioannis; Andreas ARVANITOYEORGOS a Yusuke SAKANE. Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands. International Journal of Mathematics. 2013, roč. 24, č. 10, s. 1-52. ISSN 0129-167X. Dostupné z: https://doi.org/10.1142/S0129167X13500778.

@article{1174168,
   author = {Chrysikos, Ioannis and Arvanitoyeorgos, Andreas and Sakane, Yusuke},
   article_number = {10},
   doi = {https://doi.org/10.1142/S0129167X13500778},
   keywords = {Homogeneous space; Einstein metric; Riemannian submersion; generalized flag manifold; isotropy representation; Weyl group.},
   language = {eng},
   issn = {0129-167X},
   journal = {International Journal of Mathematics},
   title = {Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands},
   url = {http://www.worldscientific.com/doi/abs/10.1142/S0129167X13500778?af=R},
   volume = {24},
   year = {2013}
}

TY  - JOUR
ID  - 1174168
AU  - Chrysikos, Ioannis - Arvanitoyeorgos, Andreas - Sakane, Yusuke
PY  - 2013
TI  - Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands
JF  - International Journal of Mathematics
VL  - 24
IS  - 10
SP  - 1-52
EP  - 1-52
SN  - 0129167X
KW  - Homogeneous space
KW  - Einstein metric
KW  - Riemannian submersion
KW  - generalized flag manifold
KW  - isotropy representation
KW  - Weyl group.
UR  - http://www.worldscientific.com/doi/abs/10.1142/S0129167X13500778?af=R
L2  - http://www.worldscientific.com/doi/abs/10.1142/S0129167X13500778?af=R
N2  - 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 is based 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.
ER  -

CHRYSIKOS, Ioannis; Andreas ARVANITOYEORGOS a Yusuke SAKANE. Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands. \textit{International Journal of Mathematics}. 2013, roč.~24, č.~10, s.~1-52. ISSN~0129-167X. Dostupné z: https://doi.org/10.1142/S0129167X13500778.

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