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

Abstract

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 © 2023 authors. All rights reserved.