| Title:
|
A characterization of the Riemann extension in terms of harmonicity (English) |
| Author:
|
Bejan, Cornelia-Livia |
| Author:
|
Eken, Şemsi |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
197-206 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
If $(M,\nabla )$ is a manifold with a symmetric linear connection, then $T^{*}M$ can be endowed with the natural Riemann extension $\bar {g}$ (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to $\bar {g}$ initiated by C. L. Bejan and O. Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure $\mathcal {P}$ on $(T^{*}M,\bar {g})$ and prove that $\mathcal {P}$ is harmonic (in the sense of E. García-Río, L. Vanhecke and M. E. Vázquez-Abal (1997)) if and only if $\bar {g}$ reduces to the classical Riemann extension introduced by E. M. Patterson and A. G. Walker (1952). (English) |
| Keyword:
|
semi-Riemannian manifold |
| Keyword:
|
cotangent bundle |
| Keyword:
|
natural Riemann extension |
| Keyword:
|
harmonic tensor field |
| MSC:
|
53B05 |
| MSC:
|
53C07 |
| MSC:
|
53C43 |
| MSC:
|
53C50 |
| MSC:
|
58E20 |
| idZBL:
|
Zbl 06738512 |
| idMR:
|
MR3633006 |
| DOI:
|
10.21136/CMJ.2017.0459-15 |
| . |
| Date available:
|
2017-03-13T12:09:16Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146048 |
| . |
| 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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