Isometric immersions of tori into \(\mathbb{R}^ 3\) with given mean curvature
It is known that a compact Riemannian surface can admit at most two geometrically distinct isometric immersions into \(\mathbb{R}^ 3\) with given non-constant mean curvature. If the genus is zero, then there is at most one such immersion. The authors consider the question if the at most two immersions can be reduced to at most one for surfaces of genus 1. A positive answer is given for three particular types of surfaces of genus 1.
scientific article; zbMATH DE number 62171