Orthogonal curvilinear coordinate systems and torsion-free sheaves over reducible spectral curves

TL;DR

This paper uses finite-gap integration methods to construct orthogonal curvilinear coordinate systems in Euclidean space linked to torsion-free sheaves over reducible spectral curves, advancing geometric and algebraic understanding.

Contribution

It introduces a novel approach connecting finite-gap integration with the construction of orthogonal coordinate systems via torsion-free sheaves on reducible spectral curves.

Findings

Constructed new classes of orthogonal coordinate systems.

Established a link between spectral curves and geometric structures.

Extended finite-gap integration techniques to reducible spectral curves.

Abstract

The methods of finite-gap integration are used to construct orthogonal curvilinear coordinate systems in the Euclidean space corresponding to sheaves of rank one without torsion over reducible singular spectral curves.