Differential invariants of Einstein-Weyl structures in 3D

JOURNAL OF GEOMETRY AND PHYSICS

卷:131

Article

Kruglikov, Boris¹  Schneider, Eivind¹ 

[1] UiT Arctic Univ Norway, Dept Math & Stat, N-9037 Tromso, Norway

关键词: Manakov-Santini equation;    Equivalence pseudogroup;    Hilbert polynomial;    Poincare function;    Lax pair;   

DOI  :  10.1016/j.geomphys.2018.05.011

来源: Elsevier

【 摘 要 】

Einstein-Weyl structures on a three-dimensional manifold M are given by a system epsilon of PDEs on sections of a bundle over M. This system is invariant under the Lie pseudogroup 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 epsilon/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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free