Applications of the Ashtekar gravity to four-dimensional hyperk{umlt a}hler geometry and Yang{endash}Mills instantons

Journal Article · Fri Oct 31 23:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532169· OSTI ID:544817

Hashimoto, Y ^[1]; Yasui, Y; Miyagi, S; Ootsuka, T ^[2]

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1. Department of Mathematics, Osaka City University, Sumiyoshiku, Osaka (Japan)
2. Department of Physics, Osaka City University, Sumiyoshiku, Osaka (Japan)

The Ashtekar{endash}Jacobson{endash}Smolin{endash}Mason{endash}Newman equations are used to construct the hyperk{umlt a}hler metrics on four-dimensional manifolds. These equations are closely related to anti-self-dual Yang{endash}Mills equations of the infinite-dimensional gauge Lie algebras of all volume-preserving vector fields. Several examples of hyperk{umlt a}hler metrics are presented through the reductions of anti-self-dual connections. For any gauge group anti-self-dual connections on hyperk{umlt a}hler manifolds are constructed using the solutions of both Nahm and Laplace equations. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 544817
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DUALITY
FOUR-DIMENSIONAL CALCULATIONS
GEOMETRY
GRAVITATION
INSTANTONS
LAPLACE EQUATION
QUANTUM GRAVITY
YANG-MILLS THEORY