New models of normal motions of the inextensible curves according to type-1 Bishop frame in ℝ3
2020 ◽
Vol 18
(01)
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pp. 2150009
Keyword(s):
In this work, we compute the time evolution equations (TEEs) of the type-1 Bishop frame of the curve. Also, we study the time evolution equations for type-1 Bishop curvatures (TEEBCs) as a system of partial differential equations (PDEs). Through this study, we give a necessary and sufficient condition for the normal and binormal Bishop velocities. Also, we construct new models of normal motions of inextensible curves in [Formula: see text]. These models are constructed for curves that move according to the type-1 Bishop frame. Also, we make a comparison study between surfaces obtained by the motions of inextensible curves according to the two frames, the type-1 Bishop frame and the Frenet frame.
2017 ◽
Vol E100.A
(12)
◽
pp. 2764-2775
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