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G3-homogeneous gravitational instantons

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 Added by Francois Bourliot
 Publication date 2009
  fields Physics
and research's language is English




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We provide an exhaustive classification of self-dual four-dimensional gravitational instantons foliated with three-dimensional homogeneous spaces, i.e. homogeneous self-dual metrics on four-dimensional Euclidean spaces admitting a Bianchi simply transitive isometry group. The classification pattern is based on the algebra homomorphisms relating the Bianchi group and the duality group SO(3). New and general solutions are found for Bianchi III.



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347 - Maciej Dunajski , Paul Tod 2019
We construct isometric and conformally isometric embeddings of some gravitational instantons in $mathbb{R}^8$ and $mathbb{R}^7$. In particular we show that the embedding class of the Einstein--Maxwell instanton due to Burns is equal to $3$. For $mathbb{CP}^2$, Eguchi--Hanson and anti-self-dual Taub-NUT we obtain upper and lower bounds on the embedding class.
93 - Yu Hamada , Jan M. Pawlowski , 2020
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226 - Maciej Dunajski , Paul Tod 2019
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