GL(2)-structures in dimension four, H-flatness and integrability

摘要

We show that torsion-free four-dimensional GL(2)-structures are flat up to a coframe transformation with a mapping taking values in a certain subgroup H subset of SL(4, N), which is isomorphic to a semidirect product of the three-dimensional continuous Heisenberg group H-3(R ) and the Abelian group N. In addition, we show that the relevant PDE system is integrable in the sense that it admits a dispersionless Lax-pair.