## Vol 23, No 2 (2019)

**Year:**2019**Articles:**11**URL:**https://journals.eco-vector.com/1991-8615/issue/view/1232

###### 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.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):207-228

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):229-245

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):246-255

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):256-269

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):270-283

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):284-303

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):304-340

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):341-360

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):361-377

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):378-393

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):394-401