  New Hamiltonian formalism based on the theory of conjugate curvilinear
coordinate nets is established. All formulas are ``mirrored'' to corresponding
formulas in the Hamiltonian formalism constructed by B.A. Dubrovin and S.P.
Novikov (in a flat case) and E.V. Ferapontov (in a non-flat case). In the
``mirrored-flat'' case the Lagrangian formulation is found. Multi-Hamiltonian
examples are presented. In particular Egorov's case, generalizations of local
Nutku--Olver's Hamiltonian structure and corresponding Sheftel--Teshukov's
recursion operator are presented. An number of Hamiltonian structures of all
odd orders is found.
