| Title:
|
On Uniqueness Theoremsfor Ricci Tensor (English) |
| Author:
|
Khripunova, Marina B. |
| Author:
|
Stepanov, Sergey E. |
| Author:
|
Tsyganok, Irina I. |
| Author:
|
Mikeš, Josef |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
47-52 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$, construct a metric on $M$ whose Ricci tensor equals $r$. In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative section curvature. In addition, we extended our result to complete non-compact Riemannian manifolds with nonnegative sectional curvature and with finite total scalar curvature. (English) |
| Keyword:
|
Uniqueness theorem for Ricci tensor |
| Keyword:
|
compact and complete Riemannian manifolds |
| Keyword:
|
vanishing theorem |
| MSC:
|
53C20 |
| idZBL:
|
Zbl 1373.53045 |
| idMR:
|
MR3674599 |
| . |
| Date available:
|
2016-08-30T11:53:27Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145816 |
| . |
| 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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| . |
