Flag manifolds, symmetric t-triples and Einstein metrics

J 2012

Flag manifolds, symmetric t-triples and Einstein metrics

CHRYSIKOS, Ioannis

Základní údaje

Originální název

Flag manifolds, symmetric t-triples and Einstein metrics

Autoři

CHRYSIKOS, Ioannis

Vydání

Differential Geometry and its Applications, Elsevier, 2012, 0926-2245

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.484

DOI

http://dx.doi.org/10.1016/j.difgeo.2012.09.001

UT WoS

000313917800008

Klíčová slova anglicky

Generalized flag manifolds; t-Roots; Symmetric t-triples; Root systems; Structure constants; Homogeneous Einstein metrics

Štítky

RIV ne

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 17. 4. 2024 09:29, Mgr. Marie Šípková, DiS.

Anotace

V originále

Let G be a compact connected simple Lie group and let M = G(C)/P = G/K be a generalized flag manifold. In this article we focus on an important invariant of G/K, the so-called t-root system R-t, and we introduce the notion of symmetric t-triples, that is triples of t-roots xi, zeta, eta is an element of R-t such that xi + eta + zeta = 0. We describe their properties and we present an interesting application on the structure constants of G/K, quantities which are straightforward related to the construction of the homogeneous Einstein metric on G/K. We classify symmetric t-triples for generalized flag manifolds G/K with second Betti number b(2)(G/K) = 1, and next we treat the case of full flag manifolds G/T, with b(2)(G/T)=l= rk G, where T is a maximal torus of G. In the last section we construct the homogeneous Einstein equation on flag manifolds G/K with five isotropy summands, determined by the simple Lie group G = SO(7). By solving the corresponding algebraic system we classify all SO(7)-invariant (non-isometric) Einstein metrics, and these are the very first results towards the classification of homogeneous Einstein metrics on flag manifolds with five isotropy summands.

Citovat

CHRYSIKOS, Ioannis. Flag manifolds, symmetric t-triples and Einstein metrics. Differential Geometry and its Applications. Elsevier, 2012, roč. 30, č. 6, s. 642-659. ISSN 0926-2245. Dostupné z: https://dx.doi.org/10.1016/j.difgeo.2012.09.001.

@article{2394731,
   author = {Chrysikos, Ioannis},
   article_number = {6},
   doi = {http://dx.doi.org/10.1016/j.difgeo.2012.09.001},
   keywords = {Generalized flag manifolds; t-Roots; Symmetric t-triples; Root systems; Structure constants; Homogeneous Einstein metrics},
   language = {eng},
   issn = {0926-2245},
   journal = {Differential Geometry and its Applications},
   title = {Flag manifolds, symmetric t-triples and Einstein metrics},
   url = {https://www.sciencedirect.com/science/article/pii/S0926224512000812},
   volume = {30},
   year = {2012}
}

TY  - JOUR
ID  - 2394731
AU  - Chrysikos, Ioannis
PY  - 2012
TI  - Flag manifolds, symmetric t-triples and Einstein metrics
JF  - Differential Geometry and its Applications
VL  - 30
IS  - 6
SP  - 642-659
EP  - 642-659
PB  - Elsevier
SN  - 09262245
KW  - Generalized flag manifolds
KW  - t-Roots
KW  - Symmetric t-triples
KW  - Root systems
KW  - Structure constants
KW  - Homogeneous Einstein metrics
UR  - https://www.sciencedirect.com/science/article/pii/S0926224512000812
N2  - Let G be a compact connected simple Lie group and let M = G(C)/P = G/K be a generalized flag manifold. In this article we focus on an important invariant of G/K, the so-called t-root system R-t, and we introduce the notion of symmetric t-triples, that is triples of t-roots xi, zeta, eta is an element of R-t such that xi + eta + zeta = 0. We describe their properties and we present an interesting application on the structure constants of G/K, quantities which are straightforward related to the construction of the homogeneous Einstein metric on G/K. We classify symmetric t-triples for generalized flag manifolds G/K with second Betti number b(2)(G/K) = 1, and next we treat the case of full flag manifolds G/T, with b(2)(G/T)=l= rk G, where T is a maximal torus of G. In the last section we construct the homogeneous Einstein equation on flag manifolds G/K with five isotropy summands, determined by the simple Lie group G = SO(7). By solving the corresponding algebraic system we classify all SO(7)-invariant (non-isometric) Einstein metrics, and these are the very first results towards the classification of homogeneous Einstein metrics on flag manifolds with five isotropy summands.
ER  -

CHRYSIKOS, Ioannis. Flag manifolds, symmetric t-triples and Einstein metrics. \textit{Differential Geometry and its Applications}. Elsevier, 2012, roč.~30, č.~6, s.~642-659. ISSN~0926-2245. Dostupné z: https://dx.doi.org/10.1016/j.difgeo.2012.09.001.

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