Classification of 4-dimensional homogeneous D'Atri spaces

Title:

Classification of 4-dimensional homogeneous D'Atri spaces

Creator:

Arias-Marco, Teresa and Kowalski, Oldřich

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:0b6a08ce-ee28-4624-8d40-2f496e45d9ac
uuid:0b6a08ce-ee28-4624-8d40-2f496e45d9ac

Subject:

Riemannian manifold, naturally reductive Riemannian homogeneous space, and D’Atri space

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The property of being a D’Atri space (i.e., a space with volume-preserving symmetries) is equivalent to the infinite number of curvature identities called the odd Ledger conditions. In particular, a Riemannian manifold $(M,g)$ satisfying the first odd Ledger condition is said to be of type $\mathcal {A}$. The classification of all 3-dimensional D’Atri spaces is well-known. All of them are locally naturally reductive. The first attempts to classify all 4-dimensional homogeneous D’Atri spaces were done in the papers by Podesta-Spiro and Bueken-Vanhecke (which are mutually complementary). The authors started with the corresponding classification of all spaces of type $\mathcal {A}$, but this classification was incomplete. Here we present the complete classification of all homogeneous spaces of type $\mathcal {A}$ in a simple and explicit form and, as a consequence, we prove correctly that all homogeneous 4-dimensional D’Atri spaces are locally naturally reductive.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

203-239

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:1

Harvested from:

CDK

Metadata only:

false