Classification of 4-dimensional homogeneous weakly einstein manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10317473" target="_blank" >RIV/00216208:11320/15:10317473 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10587-015-0159-4" target="_blank" >http://dx.doi.org/10.1007/s10587-015-0159-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10587-015-0159-4" target="_blank" >10.1007/s10587-015-0159-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Classification of 4-dimensional homogeneous weakly einstein manifolds

Popis výsledku v původním jazyce

Y.Euh, J. Park and K. Sekigawa were the first authors who defined the concept of a weakly Einstein Riemannian manifold as a modification of that of an Einstein Riemannian manifold. The defining formula is expressed in terms of the Riemannian scalar invariants of degree two. This concept was inspired by that of a super-Einstein manifold introduced earlier by A.Gray and T. J.Willmore in the context of mean-value theorems in Riemannian geometry. The dimension 4 is the most interesting case, where each Einstein space is weakly Einstein. The original authors gave two examples of homogeneous weakly Einstein manifolds (depending on one, or two parameters, respectively) which are not Einstein. The goal of this paper is to prove that these examples are the onlyexisting examples. We use, for this purpose, the classification of 4-dimensional homogeneous Riemannian manifolds given by L.B,rard Bergery and, also, the basic method and many explicit formulas from our previous article with different t

Název v anglickém jazyce

Classification of 4-dimensional homogeneous weakly einstein manifolds

Popis výsledku anglicky

Y.Euh, J. Park and K. Sekigawa were the first authors who defined the concept of a weakly Einstein Riemannian manifold as a modification of that of an Einstein Riemannian manifold. The defining formula is expressed in terms of the Riemannian scalar invariants of degree two. This concept was inspired by that of a super-Einstein manifold introduced earlier by A.Gray and T. J.Willmore in the context of mean-value theorems in Riemannian geometry. The dimension 4 is the most interesting case, where each Einstein space is weakly Einstein. The original authors gave two examples of homogeneous weakly Einstein manifolds (depending on one, or two parameters, respectively) which are not Einstein. The goal of this paper is to prove that these examples are the onlyexisting examples. We use, for this purpose, the classification of 4-dimensional homogeneous Riemannian manifolds given by L.B,rard Bergery and, also, the basic method and many explicit formulas from our previous article with different t

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GAP201%2F11%2F0356" target="_blank" >GAP201/11/0356: Riemannova, pseudo-Riemannova a afinní diferenciální geometrie</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Czechoslovak Mathematical Journal

ISSN

0011-4642

e-ISSN

—

Svazek periodika

65

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

39

Strana od-do

21-59

Kód UT WoS článku

000352820000002

EID výsledku v databázi Scopus

2-s2.0-84938081114