Differential Equations of the Space-Like Loxodromes on the Helicoidal Surfaces in Minkowski 3-Space

2017 ◽  
Vol 28 (2) ◽  
pp. 495-512
Author(s):  
Murat Babaarslan ◽  
Mustafa Kayacik
Keyword(s):  
Differential Equations ◽  
Helicoidal Surfaces

scholarly journals Generalized Helicoidal Surfaces in Euclidean 5-space

2021 ◽  
Vol 29 (3) ◽  
pp. 269-283
Author(s):  
Ali Uçum ◽  
Makoto Sakaki
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Normal Curvature ◽  
Helicoidal Surfaces ◽  
Necessary And Sufficient

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.

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