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arXiv · 1512.04035

On tube-log Riemann surfaces and primitives of rational functions

Kingshook Biswas·Ricardo Perez-Marco
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Abstract

For a generic class of rational functions, we give an explicit description of the flat structure on the Riemann sphere induced by a meromorphic 1-form R(z)dz, where R is a rational function. The rational functions in the generic class we consider have only simple poles. We show that the flat structure may be obtained by pasting isometrically flat half-cylinders to a 'log-polygon', which is a domain bounded by straight line segments in a simply connected finite sheeted branched cover of C.

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Kingshook Biswas, Ricardo Perez-Marco. 2015-12-13. On tube-log Riemann surfaces and primitives of rational functions. https://arxiv.org/abs/1512.04035

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