Classes of Bianchi equations of third order

Abstract

On the basis of determining equations written out in terms of Laplace invariants, some classes of Bianchi equations of third order similar to well-known classes of hyperbolic equations with two independent variables are singled out.

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Correspondence to A. N. Mironov.

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Original Russian Text © A. N. Mironov, 2013, published in Matematicheskie Zametki, 2013, Vol. 94, No. 3, pp. 389–400.

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Mironov, A.N. Classes of Bianchi equations of third order. Math Notes 94, 369–378 (2013). https://doi.org/10.1134/S0001434613090083

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Keywords

  • Bianchi equation of third order
  • hyperbolic equation
  • Laplace invariant
  • Lie algebra
  • Euler-Poisson equation
  • Liouville equation