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Gauge theory on projective surfaces and anti-self-dual Einstein metrics in dimension four | | Maciej Dunajski
; Thomas Mettler
; | | Date: |
14 Sep 2015 | | Abstract: | Given a projective structure on a surface N, we show how to canonically
construct a neutral signature Einstein metric with non-zero scalar curvature on
the total space M of a certain rank 2 affine bundle M->N. The resulting
Einstein metric has anti-self-dual conformal curvature and admits a parallel
field of anti-self-dual planes. We show that Einstein metrics arising from this
construction admit smooth deformations to Ricci--flat metrics if the
corresponding projective structures admit a representative connection with
totally skew-symmetric Ricci tensor. The homogeneous Einstein metric
corresponding to the flat projective structure on RP^2 is the non-compact real
form of the Fubini-Study metric on M=SL(3, R)/GL(2, R). | | Source: | arXiv, 1509.4276 | | Services: | Forum | Review | PDF | Favorites | |
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