| Title:
|
A class of metrics on tangent bundles of pseudo-Riemannian manifolds (English) |
| Author:
|
Dida, H. M. |
| Author:
|
Ikemakhen, A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
293-308 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We provide the tangent bundle $TM$ of pseudo-Riemannian manifold $(M,g)$ with the Sasaki metric $g^s$ and the neutral metric $g^n$. First we show that the holonomy group $H^s$ of $(TM ,g^s)$ contains the one of $(M,g)$. What allows us to show that if $(TM ,g^s)$ is indecomposable reducible, then the basis manifold $(M,g)$ is also indecomposable-reducible. We determine completely the holonomy group of $(TM ,g^n)$ according to the one of $(M,g)$. Secondly we found conditions on the base manifold under which $(TM ,g^s)$ ( respectively $(TM ,g^n)$ ) is Kählerian, locally symmetric or Einstein manifolds. $(TM ,g^n)$ is always reducible. We show that it is indecomposable if $(M,g)$ is irreducible. (English) |
| Keyword:
|
pseudo-Riemannian manifold |
| Keyword:
|
tangent bundle |
| Keyword:
|
Sasaki metric |
| Keyword:
|
neutral metric |
| Keyword:
|
holonomy group |
| Keyword:
|
indecomposable-reducible manifold |
| Keyword:
|
Einstein manifold |
| MSC:
|
53B30 |
| MSC:
|
53C07 |
| MSC:
|
53C29 |
| MSC:
|
53C50 |
| idZBL:
|
Zbl 1249.53020 |
| idMR:
|
MR2876951 |
| . |
| Date available:
|
2011-12-16T15:18:16Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141777 |
| . |
| Reference:
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