Abstract
In this paper, we study the geometry of the proper curve and proper helix of order 2 lying on the hyperbolic plane H20(−r), globally from Minkowski space E31. We develop the Frenet frame (orthogonal frame) along the proper curve of order 2 using connection ˜∇ on E31 and connection ∇ on H20(−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 H20(−r). Finally, we find the condition for a proper curve of order 2 with non constant curvature to become a Vk−slant helix in E31.
Funding Statement
Santosh Kumar would like to thank the UGC of India for their financial support, Ref. No. 1068/ (CSIR-UGC NET JUNE 2019).
Acknowledgments
The authors would like to express their thanks and gratitude to the referees for their valuable suggestions.
Citation
Buddhadev Pal. Santosh Kumar. "Global view of curves lying on H20(−r)⊂E31." Adv. Studies: Euro-Tbilisi Math. J. 16 (3) 41 - 52, September 2023. https://doi.org/10.32513/asetmj/193220082324
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