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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F17%3A50013409" target="_blank" >RIV/62690094:18470/17:50013409 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs10455-017-9550-8" target="_blank" >https://link.springer.com/article/10.1007%2Fs10455-017-9550-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10455-017-9550-8" target="_blank" >10.1007/s10455-017-9550-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

Let M be a cohomogeneity one manifold of a compact semisimple Lie group G with one singular orbit S-0 = G/H. Then M is G-diffeomorphic to the total space G x(H) V of the homogeneous vector bundle over S-0 defined by a sphere transitive representation of G in a vector space V. We describe all such manifolds M which admit an invariant Kahler structure of standard type. Thismeans that the restriction mu : S = Gx = G/L -&gt; F = G/K of the moment map of M to a regular orbit S = G/L is a holomorphic map of S with the induced CR structure onto a flag manifold F = G/K, where K = N-G(L), endowed with an invariant complex structure J(F). We describe all such standard Kahler cohomogeneity one manifolds in terms of the painted Dynkin diagram associated with F = G/K, J(F)) and a parameterized interval in some T-Weyl chamber. We determine which of these manifolds admit invariant Kahler-Einstein metrics.

Název v anglickém jazyce

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

Popis výsledku anglicky

Let M be a cohomogeneity one manifold of a compact semisimple Lie group G with one singular orbit S-0 = G/H. Then M is G-diffeomorphic to the total space G x(H) V of the homogeneous vector bundle over S-0 defined by a sphere transitive representation of G in a vector space V. We describe all such manifolds M which admit an invariant Kahler structure of standard type. Thismeans that the restriction mu : S = Gx = G/L -&gt; F = G/K of the moment map of M to a regular orbit S = G/L is a holomorphic map of S with the induced CR structure onto a flag manifold F = G/K, where K = N-G(L), endowed with an invariant complex structure J(F). We describe all such standard Kahler cohomogeneity one manifolds in terms of the painted Dynkin diagram associated with F = G/K, J(F)) and a parameterized interval in some T-Weyl chamber. We determine which of these manifolds admit invariant Kahler-Einstein metrics.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

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

52

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

30

Strana od-do

99-128

Kód UT WoS článku

000405297600006

EID výsledku v databázi Scopus

—