  The Gauss-Manin equations are solved for a class of flat-metrics defined by
Novikov algebras, this generalizing a result of Balinskii and Novikov who
solved this problem in the case of commutative Novikov algebras (where the
algebraic conditions reduce to those of a Frobenius algebra). The problem stems
from the theory of first-order Hamiltonian operators and their reduction to a
constant, or Darboux, form. The monodromy group associated with the Novikov
algebra gives rise to an orbit space, which is, for a wide range of Novikov
algebras, a cyclic quotient singularity.
