Second order quasilinear PDEs and conformal structures in projective space

@article{Burovskiy2008SecondOQ,
  title={Second order quasilinear PDEs and conformal structures in projective space},
  author={P. Burovskiy and E. Ferapontov and S. Tsarev},
  journal={arXiv: Exactly Solvable and Integrable Systems},
  year={2008}
}
We investigate second order quasilinear equations of the form f_{ij} u_{x_ix_j}=0 where u is a function of n independent variables x_1, ..., x_n, and the coefficients f_{ij} are functions of the first order derivatives p^1=u_{x_1}, >..., p^n=u_{x_n} only. We demonstrate that the natural equivalence group of the problem is isomorphic to SL(n+1, R), which acts by projective transformations on the space P^n with coordinates p^1, ..., p^n. The coefficient matrix f_{ij} defines on P^n a conformal… Expand
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