Lebrun manifold
{{Short description|Connected sum of copies of the complex projective plane}}
In mathematics, a LeBrun manifold is a connected sum of copies of the complex projective plane, equipped with an explicit self-dual metric. Here, self-dual means that the Weyl tensor is its own Hodge star. The metric
is determined by the choice of a finite collection of points in hyperbolic 3-space. These metrics were discovered by {{harvs|txt|last=LeBrun|first=Claude|authorlink=Claude LeBrun|year=1991}}, and named after LeBrun by {{harvs|txt|last1=Atiyah|first1=Michael|last2=Witten|first2=Edward|authorlink1=Michael Atiyah|authorlink2=Edward Witten|year=2002}}.
References
- {{Citation | last1=Atiyah | first1=Michael | author1-link=Michael Atiyah | last2=Witten | first2=Edward | author2-link=Edward Witten | title=M-theory dynamics on a manifold of G2 holonomy | arxiv=hep-th/0107177 | year=2002 | journal=Advances in Theoretical and Mathematical Physics | issn=1095-0761 | volume=6 | issue=1 | pages=1–106| bibcode=2001hep.th....7177A }}
- {{Citation | last1=LeBrun | first1=Claude | authorlink=Claude LeBrun | title=Explicit self-dual metrics on CP2#...#CP2 | url=http://projecteuclid.org/getRecord?id=euclid.jdg/1214446999 |mr=1114461 | year=1991 | journal=Journal of Differential Geometry | issn=0022-040X | volume=34 | issue=1 | pages=223–253}}