| Title:
|
Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures (English) |
| Author:
|
Ghosh, Amalendu |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
315-325 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures $(g, \pm \omega )$ with constant scalar curvature is either Einstein, or the dual field of $\omega $ is Killing. Next, let $(M^n, g)$ be a complete and connected Riemannian manifold of dimension at least $3$ admitting a pair of Einstein-Weyl structures $(g, \pm \omega )$. Then the Einstein-Weyl vector field $E$ (dual to the $1$-form $\omega $) generates an infinitesimal harmonic transformation if and only if $E$ is Killing. (English) |
| Keyword:
|
Weyl manifold |
| Keyword:
|
Einstein-Weyl structure |
| Keyword:
|
infinitesimal harmonic transformation |
| MSC:
|
53C15 |
| MSC:
|
53C20 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 06644016 |
| idMR:
|
MR3557582 |
| DOI:
|
10.21136/MB.2016.0072-14 |
| . |
| Date available:
|
2016-10-01T15:59:54Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145896 |
| . |
| Reference:
|
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