Gauge field configurations in curved spacetimes. II

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Abstract
We continue the study of gauge field configurations in curved spaces, using the formalism and results of the preceding paper. A class of static, finite-action, self-dual solutions of SU(2) gauge fields on a Euclidean section of de Sitter space is presented. The action depends on a continuous parameter. The spin-connection solution is obtained as a particular case and a certain passage to the limiting case of a flat space is shown to reproduce the Euclidean Prasad-Sommerfield solution. The significance and possible interest of such solutions are discussed. The results are then generalized to a non-Einstein but conformally flat space, including de Sitter space as an Einstein limit. Next, Bäcklund-type transformations are constructed starting from self-duality constraints for such curved spaces. These transformations are applied to the above-mentioned solutions. The last two sections contain remarks on solutions with a background Robinson-Bertotti metric and on static, axially symmetric solutions, respectively.

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