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September 2023 Global view of curves lying on H20(r)E31
Buddhadev Pal, Santosh Kumar
Adv. Studies: Euro-Tbilisi Math. J. 16(3): 41-52 (September 2023). DOI: 10.32513/asetmj/193220082324

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 Vkslant 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

Download 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

Information

Received: 23 January 2023; Accepted: 7 February 2023; Published: September 2023
First available in Project Euclid: 22 September 2023

Digital Object Identifier: 10.32513/asetmj/193220082324

Subjects:
Primary: 53C50
Secondary: 53C40

Keywords: Vkslant helix , Frenet frame , hyperbolic plane , Minkowski space , proper curve of order 2 , proper helix of order 2

Rights: Copyright © 2023 Tbilisi Centre for Mathematical Sciences

Vol.16 • No. 3 • September 2023
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