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
MSC 2010
- Primary 53A05
- Secondary 53C42
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