Hopf tori and standard tori

Abstract

This article provides a complete characterization of the conformal classes of product tori and standard flat tori in complex dimension 1 (real dimension 2). Utilizing basic differential geometry methods, our approach contrasts with techniques employing Hopf tori for the conformal classification of Riemann surfaces of genus 1. While the results may be familiar to experts in complex analysis and Riemann surface theory, we contend that this work offers a clear and insightful perspective on the conformal properties of these geometrically distinct appearing tori.