We find exact multi-instanton solutions to the self-dual Yang–Mills equation on a large class of curved spaces with SO(3) isometry, generalizing the results previously found on ℝ4. The solutions are featured with explicit multi-centered expressions and topological properties. As examples, we demonstrate the approach on several different curved spaces, including the Einstein static universe and ℝ ×dS3E, and show that the exact multi-instanton solutions exist on these curved backgrounds.

中文翻译：

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弯曲空间上自对偶 Yang-Mills 方程的精确多瞬时解

我们在一大类弯曲空间上找到了自对偶 Yang-Mills 方程的精确多瞬时解小号○(3)等距，概括先前发现的结果ℝ4. 解决方案具有明确的多中心表达式和拓扑属性。作为示例，我们在几个不同的弯曲空间上演示了该方法，包括爱因斯坦静态宇宙和ℝ ×dS3乙，并表明在这些弯曲的背景上存在精确的多实例解。