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This article is cited in 1 scientific paper (total in 1 paper)
Differential Equations and Mathematical Physics
Duality equations on a 4-manifold of conformal torsion-free connection and some of their solutions for the zero signature
L. N. Krivonosov, V. A. Lukyanov Nizhny Novgorod State Technical University, Nizhnii Novgorod, 603600, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
On a 4-manifold of conformal torsion-free connection with zero signature $( --++) $ we found conditions under which the conformal curvature matrix is dual (self-dual or anti-self-dual). These conditions are 5 partial differential equations of the 2nd order on 10 coefficients of the angular metric and 4 partial differential equations of the 1st order, containing also 3 coefficients of external 2-form of charge. (External 2-form of charge is one of the components of the conformal curvature matrix.) Duality equations for a metric of a diagonal type are composed. They form a system of five second-order differential equations on three unknown functions of all four variables. We found several series of solutions for this system. In particular, we obtained all solutions for a logarithmically polynomial diagonal metric, that is, for a metric whose coefficients are exponents of polynomials of four variables.
Keywords:
manifold of conformal connection, curvature, torsion, Hodge operator, self-duality, anti-self-duality, Yang–Mills equations.
Received: January 23, 2019 Revised: May 12, 2019 Accepted: June 10, 2019 First online: June 12, 2019
Citation:
L. N. Krivonosov, V. A. Lukyanov, “Duality equations on a 4-manifold of conformal torsion-free connection and some of their solutions for the zero signature”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:2 (2019), 207–228
Linking options:
https://www.mathnet.ru/eng/vsgtu1674 https://www.mathnet.ru/eng/vsgtu/v223/i2/p207
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