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

Authors : Buddhadev PAL, Santosh KUMAR

Pages : 1288-1303

Doi:10.15672/hujms.960966

View : 27 | Download : 15

Publication Date : 2022-10-01

Article Type : Research Paper

Abstract :In this paper, we analyse the proper curve $\gammainsert ignore into journalissuearticles values(s);$ lying on the pseudo-sphere. We develop an orthogonal frame $\lbrace V_{1}, V_{2}, V_{3} \rbrace$ along the proper curve, lying on pseudosphere. Next, we find the condition for $\gammainsert ignore into journalissuearticles values(s);$ to become $V_{k} -$ slant helix in Minkowski space. Moreover, we find another curve $\betainsert ignore into journalissuearticles values(\bar{s});$ lying on pseudosphere or hyperbolic plane heaving $V_{2} = \bar{V_{2}}$ for which $\lbrace \bar{V_{1}},\bar{V_{2}},\bar{V_{3}} \rbrace$, an orthogonal frame along $\betainsert ignore into journalissuearticles values(\bar{s});$. Finally, we find the condition for curve $\gammainsert ignore into journalissuearticles values(s);$ to lie in a plane.
Keywords : Minkowski space, pseudo sphere, proper helix of order 2, proper curve of order 2, V k slant helix