| Title:
|
A curvature identity on a 6-dimensional Riemannian manifold and its applications (English) |
| Author:
|
Euh, Yunhee |
| Author:
|
Park, Jeong Hyeong |
| Author:
|
Sekigawa, Kouei |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
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1572-9141 (online) |
| Volume:
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67 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
253-270 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold ``a harmonic manifold is locally symmetric'' and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a slightly more general setting.\looseness -1 (English) |
| Keyword:
|
Chern-Gauss-Bonnet theorem |
| Keyword:
|
curvature identity |
| Keyword:
|
locally harmonic manifold |
| MSC:
|
53B20 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 06738516 |
| idMR:
|
MR3633010 |
| DOI:
|
10.21136/CMJ.2017.0540-15 |
| . |
| Date available:
|
2017-03-13T12:11:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146052 |
| . |
| Reference:
|
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| Reference:
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