| Title:
|
A new variational characterization of compact conformally flat 4-manifolds (English) |
| Author:
|
Wu, Faen |
| Author:
|
Zhao, Xinnuan |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
20 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
71-77 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we give a new variational characterization of certain 4-manifolds. More precisely, let $R$ and $Ric$ denote the scalar curvature and Ricci curvature respectively of a Riemannian metric, we prove that if $(M^{4},g)$ is compact and locally conformally flat and $g$ is the critical point of the functional $$ F(g)=\int _{M^{4}}(aR^{2}+b|Ric|^{2})\,\mathrm {d}v_{g}\,,$$ where $$(a,b)\in \mathbb {R}^{2}\setminus L_{1}\cup L_{2}$$ $$L_{1}\colon 3a+b=0\,;\quad L_{2}\colon 6a-b+1=0\,,$$ then $(M^{4},g)$ is either scalar flat or a space form. (English) |
| Keyword:
|
conformally flat |
| Keyword:
|
4-manifold |
| Keyword:
|
variational characterization |
| MSC:
|
53C20 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 06165035 |
| idMR:
|
MR3032804 |
| . |
| Date available:
|
2013-01-28T10:19:05Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143138 |
| . |
| Reference:
|
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| Reference:
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| . |
