1996/10/22 by Yoshitake Hashimoto, Y. Hashimoto, Y. Yasui +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #hep-th
paper · pdf · doi:10.1063/1.532169
published as J.Math.Phys. 38 (1997) 5833-5839 · 9pages, Figures are not included
arxiv created 1996/10/22 · openalex publication_date 1997/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Ashtekar–Jacobson–Smolin–Mason–Newman equations are used to construct the hyperkähler metrics on four-dimensional manifolds. These equations are closely related to anti-self-dual Yang–Mills equations of the infinite-dimensional gauge Lie algebras of all volume-preserving vector fields. Several examples of hyperkähler metrics are presented through the reductions of anti-self-dual connections. For any gauge group anti-self-dual connections on hyperkähler manifolds are constructed using the solutions of both Nahm and Laplace equations.