Cohomogeneity one Kahler and Kahler-Einstein manifolds with one singular orbit II

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017267" target="_blank" >RIV/62690094:18470/20:50017267 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10455-019-09693-6" target="_blank" >https://link.springer.com/article/10.1007/s10455-019-09693-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10455-019-09693-6" target="_blank" >10.1007/s10455-019-09693-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cohomogeneity one Kahler and Kahler-Einstein manifolds with one singular orbit II

Popis výsledku v původním jazyce

Podesta and Spiro (Osaka J Math 36(4):805-833, 1999) introduced a class of G-manifolds M with a cohomogeneity one action of a compact semisimple Lie group G which admit an invariant Kahler structure (g, J) (&quot;standard G-manifolds&quot;) and studied invariant Kahler and Kahler-Einstein metrics on M. In the first part of this paper, we gave a combinatoric description of the standard non-compact G-manifolds as the total space M-phi of the homogeneous vector bundle M = G x (H) V -&gt; S-0 = G/ H over a flag manifold S-0 and we gave necessary and sufficient conditions for the existence of an invariant Kahler-Einstein metric g on such manifolds M in terms of the existence of an interval in the T-Weyl chamber of the flag manifold F = G x (H) PV which satisfies some linear condition. In this paper, we consider standard cohomogeneity one manifolds of a classical simply connected Lie group G = SUn, Sp(n).Spin(n) and reformulate these necessary and sufficient conditions in terms of easily checked arithmetic properties of the Koszul numbers associated with the flag manifold S-0 = G/H. If this condition is fulfilled, the explicit construction of the Kahler-Einstein metric reduces to the calculation of the inverse function to a given function of one variable.

Název v anglickém jazyce

Cohomogeneity one Kahler and Kahler-Einstein manifolds with one singular orbit II

Popis výsledku anglicky

Podesta and Spiro (Osaka J Math 36(4):805-833, 1999) introduced a class of G-manifolds M with a cohomogeneity one action of a compact semisimple Lie group G which admit an invariant Kahler structure (g, J) (&quot;standard G-manifolds&quot;) and studied invariant Kahler and Kahler-Einstein metrics on M. In the first part of this paper, we gave a combinatoric description of the standard non-compact G-manifolds as the total space M-phi of the homogeneous vector bundle M = G x (H) V -&gt; S-0 = G/ H over a flag manifold S-0 and we gave necessary and sufficient conditions for the existence of an invariant Kahler-Einstein metric g on such manifolds M in terms of the existence of an interval in the T-Weyl chamber of the flag manifold F = G x (H) PV which satisfies some linear condition. In this paper, we consider standard cohomogeneity one manifolds of a classical simply connected Lie group G = SUn, Sp(n).Spin(n) and reformulate these necessary and sufficient conditions in terms of easily checked arithmetic properties of the Koszul numbers associated with the flag manifold S-0 = G/H. If this condition is fulfilled, the explicit construction of the Kahler-Einstein metric reduces to the calculation of the inverse function to a given function of one variable.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-00496S" target="_blank" >GA18-00496S: Singulární prostory ze speciální holonomie a foliací</a><br>

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY

ISSN

0232-704X

e-ISSN

—

Svazek periodika

57

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

22

Strana od-do

153-174

Kód UT WoS článku

000512099900007

EID výsledku v databázi Scopus

—