Einstein-Weyl spaces and third-order differential equations (Q2738132)
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scientific article; zbMATH DE number 1639306
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Einstein-Weyl spaces and third-order differential equations |
scientific article; zbMATH DE number 1639306 |
Statements
30 August 2001
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conformal manifold
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Einstein-Weyl geometry
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Einstein-Weyl spaces and third-order differential equations (English)
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The author extends the three-dimensional null-surface formalism of Tanimoto and Forni-Iriondo-Kozamech for describing Einstein-Weyl spaces and it appears that, as is mentioned in the paper, ``it was by something equivalent to the null-surface formalism that Cartan was led to discover (or invent) Einstein-Weyl geometry''. In fact, it is shown that given a differential equation of the form \(y''' = f(x,y,y',y'')\), the manifold of solutions \(y(x)\) to this equation has a canonical Einstein-Weyl structure. The author uses this construction to obtain some new examples of Einstein-Weyl manifolds.
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