  Remarkable parallelism between the theory of integrable systems of
first-order quasilinear PDE and some old results in projective and affine
differential geometry of conjugate nets, Laplace equations, their
Bianchi-Baecklund transformations is exposed.
  These results were recently applied by I.M.Krichever and B.A.Dubrovin to
prove integrability of some models in topological field theories. Within the
geometric framework we derive some new integrable (in a sense to be discussed)
generalizations describing N-wave resonant interactions.
