A certain two-parameter family of helices of order 6 in Euclidean sphere

Maeda, Satoshi; Kim, Byung Hak

doi:10.1016/j.difgeo.2014.01.011

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2022

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“…Getting motivation from the above papers [2,12], we organize our paper as follows: In Section 2, we discuss some basic concepts and results. Section 3, we study the global view of the helix of proper order 2 lying on pseudosphere of radius r from E 3 1 .…”

Section: Introductionmentioning

confidence: 99%

Characterization of proper curves and proper helix lying on $S_{1}^2(r)$

PAL

Kumar

2022

Hacettepe Journal of Mathematics and Statistics

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In this paper, we analyse the proper curve γ(s) lying on the pseudo-sphere. We develop an orthogonal frame {V 1 , V 2 , V 3 } along the proper curve, lying on pseudosphere. Next, we find the condition for γ(s) to become V k − slant helix in Minkowski space. Moreover, we find another curve β(s) lying on pseudosphere or hyperbolic plane heaving V 2 = V2 for which { V1 , V2 , V3 }, an orthogonal frame along β(s). Finally, we find the condition for curve γ(s) to lie in a plane.

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Section: Introductionmentioning

confidence: 99%