| Title:
|
Classification of 4-dimensional homogeneous D'Atri spaces (English) |
| Author:
|
Arias-Marco, Teresa |
| Author:
|
Kowalski, Oldřich |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
203-239 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Riemannian manifold |
| Keyword:
|
naturally reductive Riemannian homogeneous space |
| Keyword:
|
D’Atri space |
| MSC:
|
53B21 |
| MSC:
|
53C21 |
| MSC:
|
53C25 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 1174.53024 |
| idMR:
|
MR2402535 |
| . |
| Date available:
|
2009-09-24T11:54:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128255 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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