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arXiv · hep-th/9610069

Applications of the Ashtekar gravity to four dimensional hyperkähler geometry and Yang-Mills Instantons

Y. Hashimoto·Y. Yasui·S. Miyagi·T. Otsuka
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Abstract

The Ashtekar-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.

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Y. Hashimoto, Y. Yasui, S. Miyagi, T. Otsuka. 1996-10-22. Applications of the Ashtekar gravity to four dimensional hyperkähler geometry and Yang-Mills Instantons. https://doi.org/10.1063/1.532169

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