| Title:
|
Conformally geodesic mappings satisfying a certain initial condition (English) |
| Author:
|
Chudá, Hana |
| Author:
|
Mikeš, Josef |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
5 |
| Year:
|
2011 |
| Pages:
|
389-394 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study conformally geodesic mappings between pseudo-Riemannian manifolds $(M, g)$ and $(\bar{M}, \bar{g})$, i.e. mappings $f\colon M \rightarrow \bar{M}$ satisfying $f = f_1 \circ f_2 \circ f_3$, where $f_1, f_3$ are conformal mappings and $f_2$ is a geodesic mapping. Suppose that the initial condition $f^* \bar{g} = k g$ is satisfied at a point $x_0 \in M$ and that at this point the conformal Weyl tensor does not vanish. We prove that then $f$ is necessarily conformal. (English) |
| Keyword:
|
conformal mappings |
| Keyword:
|
geodesic mappings |
| Keyword:
|
conformally geodesic mappings |
| MSC:
|
53B20 |
| MSC:
|
53B30 |
| MSC:
|
53C21 |
| idZBL:
|
Zbl 1265.53019 |
| idMR:
|
MR2876942 |
| . |
| Date available:
|
2011-12-16T15:26:51Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141786 |
| . |
| 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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| Reference:
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| Reference:
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| Reference:
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| . |
