Complete nonorientable minimal surfaces and symmetries
The authors present new examples of complete nonorientable minimal surfaces in \(\mathbb{R}^3\) with only one end and finite total curvature. To be more precise, they construct infinite families of such surfaces, calculate their Euler-Poincaré characteristic as well as their total curvature, and describe their symmetry groups. Moreover, they show that these surfaces are unique and maximal with respect to the total curvature. The main tool for the construction is the Weierstraß representation formula. A special case is the complete minimal once-punctured Klein bottle with total curvature \(-8\pi\) originally discovered by the first author [ibid. 71, No. 1, 23-30 (1993; Zbl 0796.53006)].
scientific article; zbMATH DE number 878411
scientific article