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Differential invariants of Einstein-Weyl structures in 3D. (English) Zbl 1392.53054
Summary: Einstein-Weyl structures on a three-dimensional manifold \(M\) are given by a system \(\mathcal{E}\) of PDEs on sections of a bundle over \(M\). This system is invariant under the Lie pseudogroup \(\mathcal{G}\) of local diffeomorphisms on \(M\). Two Einstein-Weyl structures are locally equivalent if there exists a local diffeomorphism taking one to the other. Our goal is to describe the quotient equation \(\mathcal{E} / \mathcal{G}\) whose solutions correspond to nonequivalent Einstein-Weyl structures. The approach uses symmetries of the Manakov-Santini integrable system and the action of the corresponding Lie pseudogroup.
MSC:
53C20 Global Riemannian geometry, including pinching
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
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