Lévy Laplacians and instantons on manifolds
2020 ◽
Vol 23
(02)
◽
pp. 2050008
Keyword(s):
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 [Formula: see text] 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.
2019 ◽
Vol 22
(01)
◽
pp. 1950001
◽
2017 ◽
Vol 20
(02)
◽
pp. 1750008
◽
1988 ◽
Vol 108
(3-4)
◽
pp. 189-200
2000 ◽
Vol 89
(2)
◽
pp. 213-226
◽
2002 ◽
Vol 17
(08)
◽
pp. 481-489
◽
2006 ◽
Vol 21
(23n24)
◽
pp. 4931-4957
◽
Keyword(s):
2016 ◽
Vol 161
(2)
◽
pp. 357-377
Keyword(s):