FLAT STRUCTURES WITHOUT POTENTIALS

Flat structures are formulated by K. Saito in the course of the study of moduli spaces of isolated singularities. The purpose of this paper is to study flat structures without potentials, to formulate one of generalisations of ordinary differential equations of Okubo type to several variables case and to give examples of potential vector fields related with algebraic solutions of Painleve VI, free divisors arising from 1-parameter deformations of singularities on plane curves and discriminants of complex reflection groups.