| Title:
|
Deformations of Metrics and Biharmonic Maps (English) |
| Author:
|
Benkartab, Aicha |
| Author:
|
Cherif, Ahmed Mohammed |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
28 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
263-275 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct biharmonic non-harmonic maps between Riemannian manifolds $(M,g)$ and $(N,h)$ by first making the ansatz that $\varphi \colon (M,g) \rightarrow (N,h)$ be a harmonic map and then deforming the metric on $N$ by $$\tilde {h}_{\alpha }=\alpha h+(1-\alpha )df\otimes df$$ to render $\varphi $ biharmonic, where $f$ is a smooth function with gradient of constant norm on $(N,h)$ and $\alpha \in (0,1)$. We construct new examples of biharmonic non-harmonic maps, and we characterize the biharmonicity of some curves on Riemannian manifolds. (English) |
| Keyword:
|
Riemannian geometry |
| Keyword:
|
Harmonic maps |
| Keyword:
|
Biharmonic maps |
| MSC:
|
53C20 |
| MSC:
|
53C22 |
| MSC:
|
58E20 |
| idZBL:
|
Zbl 1480.53051 |
| idMR:
|
MR4197078 |
| . |
| Date available:
|
2021-03-03T08:56:33Z |
| Last updated:
|
2022-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148707 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| . |
