  We investigate the dispersionless Veselov-Novikov (dVN) equation based on the
framework of dispersionless two-component BKP hierarchy. Symmetry constraints
for real dVN system are considered. It is shown that under symmetry reductions,
the conserved densities are therefore related to the associated Faber
polynomials and can be solved recursively. Moreover, the method of hodograph
transformation as well as the expressions of Faber polynomials are used to find
exact real solutions of the dVN hierarchy.
