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Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures

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

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Publisher copy:
10.1016/j.difgeo.2016.12.003

Authors


Dunajski, M More by this author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
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

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