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 Claude LeBrun (1991), and named after LeBrun by Michael Atiyah and Edward Witten (2002).

## References

* Atiyah, Michael; Witten, Edward (2002), "M-theory dynamics on a manifold of G2 holonomy", Advances in Theoretical and Mathematical Physics 6 (1): 1–106, ISSN 1095-0761, Bibcode: 2001hep.th....7177A
* LeBrun, Claude (1991), "Explicit self-dual metrics on CP2#...#CP2", Journal of Differential Geometry 34 (1): 223–253, ISSN 0022-040X, http://projecteuclid.org/getRecord?id=euclid.jdg/1214446999

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