Lobachevskii J. Math., 2019, Volume 40, Number 10, Pages 1619–1630
Levy Laplacian on manifold and Yang–Mills heat flow
B. O. Volkovab
a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, 119991 Russia
b Bauman Moscow State Technical University, Moscow, 105005 Russia
A covariant definition of the Levy Laplacian on an infinite dimensional manifold is introduced. It is shown that a time-depended connection in a finite dimensional vector bundle is a solution of the Yang–Mills heat equations if and only if the associated flow of the parallel transports is a solution of the heat equation for the covariant Levy Laplacian on the infinite dimensional manifold.
Levy Laplacian, Yang–Mills equations, Yang–Mills heat equations, infinite dimensional manifold.
|Russian Science Foundation
|This work was supported by the Russian Science Foundation under grant 19-11-00320.
Revised version: 13.05.2019
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