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Lévy Laplacians and instantons on manifolds

Boris O. Volkov

Steklov Mathematical Institute, ul. Gubkina, 8, Moscow 119991, Russia

E-mail Address: borisvolkov1986@gmail.com

https://doi.org/10.1142/S0219025720500083Cited by:3 (Source: Crossref)

Abstract

The equivalence of the anti-selfduality Yang–Mills equations on the four-dimensional orientable Riemannian manifold and the Laplace equations for some infinite-dimensional Laplacians is proved. A class of modified Lévy 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 modified Lévy Laplacians from this class.

Communicated by Oleg Smolyanov

Dedicated to the memory of Alexander A. Belyaev

Keywords:

AMSC: 70S15, 58J35

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