Abstract: The properties of surfaces have always been a hot issue in the study of differential geometry, and cylindrical solenoid is the most important curve in the geometry. In this paper, differential geometry methods are used to investigate the geometric properties related to the principal normal surfaces of cylindrical solenoids, with the cylindrical solenoid as the object. The study has obtained conclusions on the asymptotic curves, lines of curvature, normal curvature, principal curvature, Gaussian curvature and mean curvature of the principal normal surfaces of cylindrical solenoids. The results of the study provide a basis for deepening study on the main normal surface subfluidization of cylindrical solenoid.

Key words: cylindrical spiral, principal normal surface, average curvature, Gaussian curvature, principal curvature