| Title:
|
On metrics of positive Ricci curvature conformal to $M\times \mathbf{R}^m$ (English) |
| Author:
|
Ruiz, Juan Miguel |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
105-113 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(M^n,g)$ be a closed Riemannian manifold and $g_E$ the Euclidean metric. We show that for $m>1$, $\left(M^n \times \mathbf{R}^m, (g+g_E)\right)$ is not conformal to a positive Einstein manifold. Moreover, $\left(M^n \times \mathbf{R}^m, (g+g_E)\right)$ is not conformal to a Riemannian manifold of positive Ricci curvature, through a radial, integrable, smooth function, $\varphi \colon \mathbf{R^m} \rightarrow \mathbf{R^+}$, for $m>1$. These results are motivated by some recent questions on Yamabe constants. (English) |
| Keyword:
|
conformally Einstein manifolds |
| Keyword:
|
positive Ricci curvature |
| MSC:
|
53A30 |
| MSC:
|
53C21 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 1212.53015 |
| idMR:
|
MR2591667 |
| . |
| Date available:
|
2009-06-25T18:16:35Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128293 |
| . |
| 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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| Reference:
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| Reference:
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| Reference:
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| . |
