- Abstract:
- Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in a basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possibilities. In particular we construct new examples of neutral signature non-diagonal Bianchi type VIII Einstein metrics with self-dual Weyl tensor.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
- Version:
- Accepted Manuscript
- Files:
-
-
(pdf, 114.5kb)
-
- Publisher copy:
- 10.1016/j.difgeo.2016.12.003
-
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- Publisher:
- Elsevier Publisher's website
- Journal:
- Differential Geometry and its Applications Journal website
- Volume:
- 54
- Issue:
- A
- Pages:
- 11-30
- Publication date:
- 2017-01-05
- DOI:
- ISSN:
-
0926-2245
- Pubs id:
-
pubs:824077
- URN:
-
uri:c9f9b72b-0dd3-4025-a1f5-982b51740f3c
- UUID:
-
uuid:c9f9b72b-0dd3-4025-a1f5-982b51740f3c
- Local pid:
- pubs:824077
- Copyright holder:
- Elsevier B.V.
- Copyright date:
- 2017
- Notes:
-
Copyright © 2016 Elsevier B.V. This is the accepted manuscript version of the article. The final version is available online from Elsevier at: https://doi.org/10.1016/j.difgeo.2016.12.003
Journal article
Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures
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