Vol 23, No 2 (2019)
- Year: 2019
- Articles: 11
- URL: https://journals.eco-vector.com/1991-8615/issue/view/1232
Duality equations on a 4-manifold of conformal torsion-free connection and some of their solutions for the zero signature
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.



Solvability of a nonlocal problem for a hyperbolic equation with degenerate integral conditions
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Asymmetric tensor representations in micropolar continuum mechanics theories
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Estimation of mechanical characteristics of salt rock crystals based on the mathematical model of nanoindentation using scanning probe microscope Dimension Icon
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Creep and plastic flow of a spherical viscoelastic layer material at its loading and unloading
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Determination of elastic constants of rocks
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Analysis of the linear viscoelasticity theory capabilities to simulate hydrostatic pressure influence on creep curves and lateral contraction ratio of rheonomous materials
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Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation
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Effective computational procedure of the alternance optimization method
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The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator
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On singular solutions of a multidimensional differential equation of Clairaut-type with power and exponential functions
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