Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean 3-space

Abstract

In this paper, we study the singularities on a non-developable ruled surface according to Blaschke's frame in the Euclidean 3-space. Additionally, we prove that singular points occur on this kind of ruled surface and use the singularity theory technique to examine these singularities. Finally, we construct an example to confirm and demonstrate our primary finding.

Keywords

• blaschke frame
• geodesic curvature
• singularity theory
• spherical indicatrix
• ruled surfaces