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, arXiv:hep-th/0107177, Bibcode:2001hep.th....7177A, ISSN 1095-0761
• LeBrun, Claude (1991), "Explicit self-dual metrics on CP₂#...#CP₂", Journal of Differential Geometry, 34 (1): 223–253, ISSN 0022-040X, MR 1114461