流形上的Levy Laplacian和瞬子
Levy Laplacians and instantons on manifolds
摘要：
证明了四维可定向黎曼流形上的反自对偶Yang-Mills方程与某些无穷维Laplace算子的Laplace方程的等价性。引入了一类通过选择$SO(4)$中的一条曲线来参数化的修正Levy Laplacian算子.证明了一个联络是瞬子（反自对偶Yang-Mills方程的解）当且仅当由该联络推广的平行输运是Laplace方程的解，其中有三个来自这类的修正Levy Laplacian.
英文摘要：
The equivalence of the anti-selfduality Yang-Mills equations on the 4-dimensional orientable Riemannian manifold and Laplace equations for some infinite dimensional Laplacians is proved. A class of modificated Levy Laplacians parameterized by the choice of a curve in the group $SO(4)$ is introduced. It is shown that a connection is an instanton (a solution of the anti-selfduality Yang-Mills equations) if and only if the parallel transport generalized by this connection is a solution of the Laplace equations for some three modificated Levy Laplacians from this class.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
