Generalized Helicoidal Surfaces in Euclidean 5-space

Abstract

In this paper, we study generalized helicoidal surfaces in Euclidean 5-space. We obtain the necessary and sufficient conditions for generalized helicoidal surfaces in Euclidean 5-space to be minimal, flat or of zero normal curvature tensor, which are ordinary differential equations. We solve those equations and discuss the completeness of the surfaces.

Keywords

• helicoidal surface
• minimal surface
• flat surface
• normal curvature tensor
• complete surface
• primary 53a05
• secondary 53c42