Global view of curves lying on H02(-r) ⊂ E13

B. Pal, S. Kumar

In this paper, we study the geometry of the proper curve and proper helix of order 2 lying on the hyperbolic plane H02(-r), globally from Minkowski space E13. We develop the Frenet frame (orthogonal frame) along the proper curve of order 2 using connection ∇ on E13 and connection ∇ on H02(-r). The Frenet frame for the proper curve and proper helix of order 2 depends on the curvature of the proper curve and proper helix of order 2 in the hyperbolic plane H02(-r). Finally, we find the condition for a proper curve of order 2 with non constant curvature to become a Vk-slant helix in E13. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16(3) (2023), pp. 41-52