On the Riemannian and Einstein-Weyl Geometry in Theory of the Second Order Ordinary Differential Equations

Some properties of the 4-dim Riemannian spaces with metrics $d s^{2} = 2 (z a_{3} - t a_{4}) d x^{2} + 4 (z a_{2} - t a_{3}) d x d y + 2 (z a_{1} - t a_{2}) d y^{2} + 2 d x d z + 2 d y d t$ associated with the second order nonlinear differential equations $y^{''} + a_{1} (x, y) {y^{'}}^{3} + 3 a_{2} (x, y) {y^{'}}^{2} + 3 a_{3} (x, y) y^{'} + a_{4} (x, y) = 0$ with arbitrary coefficients $a_{i} (x, y)$ and 3-dim Einstein-Weyl spaces connected with dual equations $b^{''} = g (a, b, b^{'})$ where the function $g (a, b, b^{'})$ satisfied the partial differential equation $g_{a a c c} + 2 c g_{a b c c} + 2 g g_{a c c c} + c^{2} g_{b b c c} + 2 c g g_{b c c c} + g^{2} g_{c c c c} + (g_{a} + c g_{b}) g_{c c c} - 4 g_{a b c} -$ $- 4 c g_{b b c} - c g_{c} g_{b c c} - 3 g g_{b c c} - g_{c} g_{a c c} + 4 g_{c} g_{b c} - 3 g_{b} g_{c c} + 6 g_{b b} = 0$ are considered.

On the Riemannian and Einstein-Weyl Geometry in Theory of the Second Order Ordinary Differential Equations

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On the Riemannian and Einstein-Weyl Geometry in Theory of the Second Order Ordinary Differential Equations

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On the Riemannian and Einstein-Weyl Geometry in Theory of the Second Order Ordinary Differential Equations

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On the Riemannian and Einstein-Weyl Geometry in Theory of the Second Order Ordinary Differential Equations

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|AI智能校验

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