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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2019, Volume 23, Number 2, Pages 207–228
DOI: https://doi.org/10.14498/vsgtu1674
(Mi vsgtu1674)
 

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
Full-text PDF (989 kB) Citations (1)
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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
Bibliographic databases:
Document Type: Article
UDC: 514.756.2
MSC: 53A30
Language: Russian
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
Citation in format AMSBIB
\Bibitem{KriLuk19}
\by L.~N.~Krivonosov, V.~A.~Lukyanov
\paper Duality equations on a 4-manifold of conformal torsion-free connection and some of their solutions for the zero signature
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2019
\vol 23
\issue 2
\pages 207--228
\mathnet{http://mi.mathnet.ru/vsgtu1674}
\crossref{https://doi.org/10.14498/vsgtu1674}
\elib{https://elibrary.ru/item.asp?id=41271050}
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  • https://www.mathnet.ru/eng/vsgtu/v223/i2/p207
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Full-text PDF :202
    References:46
     
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