Algebraic-geometrical n-orthogonal curvilinear coordinate systems and solutions to the associativity equations

Abstract

Algebraic-geometrical n-orthogonal curvilinear coordinate systems in a flat space are constructed. They are expressed in terms of the Riemann theta function of auxiliary algebraic curves. The exact formulae for the potentials of algebraic geometrical Egoroff metrics and the partition functions of the corresponding topological field theories are obtained.

25 pages, Latex

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