Homogeneous Einstein metrics on non-Kahler C-spaces

J 2021

Homogeneous Einstein metrics on non-Kahler C-spaces

CHRYSIKOS, Ioannis a Yusuke SAKANE

Základní údaje

Originální název

Homogeneous Einstein metrics on non-Kahler C-spaces

Autoři

CHRYSIKOS, Ioannis a Yusuke SAKANE

Vydání

Journal of Geometry and Physics, Amsterdam, Elsevier Science BV, 2021, 0393-0440

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: 1.380

Označené pro přenos do RIV

Klíčová slova anglicky

Homogeneous spaces; Invariant Einstein metrics; Non-Kahler C-spaces; Torus bundles

Štítky

RIV ne

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 26. 5. 2023 11:27, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Citovat

CHRYSIKOS, Ioannis a Yusuke SAKANE. Homogeneous Einstein metrics on non-Kahler C-spaces. Journal of Geometry and Physics. Amsterdam: Elsevier Science BV, 2021, roč. 160, February, s. 1-31. ISSN 0393-0440. Dostupné z: https://doi.org/10.1016/j.geomphys.2020.103996.

@article{2285877,
   author = {Chrysikos, Ioannis and Sakane, Yusuke},
   article_location = {Amsterdam},
   article_number = {February},
   doi = {https://doi.org/10.1016/j.geomphys.2020.103996},
   keywords = {Homogeneous spaces; Invariant Einstein metrics; Non-Kahler C-spaces; Torus bundles},
   language = {eng},
   issn = {0393-0440},
   journal = {Journal of Geometry and Physics},
   note = {Nedovádět do RIV. Afiliace je mimo MU.},
   title = {Homogeneous Einstein metrics on non-Kahler C-spaces},
   url = {https://doi.org/10.1016/j.geomphys.2020.103996},
   volume = {160},
   year = {2021}
}

TY  - JOUR
ID  - 2285877
AU  - Chrysikos, Ioannis - Sakane, Yusuke
PY  - 2021
TI  - Homogeneous Einstein metrics on non-Kahler C-spaces
JF  - Journal of Geometry and Physics
VL  - 160
IS  - February
SP  - 1-31
EP  - 1-31
PB  - Elsevier Science BV
SN  - 03930440
N1  - Nedovádět do RIV. Afiliace je mimo MU.
KW  - Homogeneous spaces
KW  - Invariant Einstein metrics
KW  - Non-Kahler C-spaces
KW  - Torus bundles
UR  - https://doi.org/10.1016/j.geomphys.2020.103996
N2  - 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.
ER  -

CHRYSIKOS, Ioannis a Yusuke SAKANE. Homogeneous Einstein metrics on non-Kahler C-spaces. \textit{Journal of Geometry and Physics}. Amsterdam: Elsevier Science BV, 2021, roč.~160, February, s.~1-31. ISSN~0393-0440. Dostupné z: https://doi.org/10.1016/j.geomphys.2020.103996.

Přehled o publikaci