Classification of 4-dimensional homogeneous weakly einstein manifolds

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Classification of 4-dimensional homogeneous weakly einstein manifolds

Original language description

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

Czech name

—

Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GAP201%2F11%2F0356" target="_blank" >GAP201/11/0356: Riemannian, pseudo-Riemannian and affine differential geometry</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2015

Confidentiality

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

Name of the periodical

Czechoslovak Mathematical Journal

ISSN

0011-4642

e-ISSN

—

Volume of the periodical

65

Issue of the periodical within the volume

1

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

39

Pages from-to

21-59

UT code for WoS article

000352820000002

EID of the result in the Scopus database

2-s2.0-84938081114