Surfaces which contain helical geodesics
Extending a result obtained jointly with \textit{N. Takeuchi} in Bull. Tokyo Gakugei Univ., Sect. IV., Math. Nat. Sci. 43, 5-8 (1991; Zbl 0755.53003) the author characterizes the type of a complete smooth surface of constant mean curvature \(M\) in \(E^ 3\) which contains many helical geodesics. The circular cylinder is characterized by the property that through each point there passes a non-straight helical geodesic under the additional condition that there are no umbilics on \(M\). The assumption of two helical geodesics through each points leads to a plane, a sphere or a circular cylinder.
scientific article; zbMATH DE number 58797