Characterization of proper curves and proper helix lying on S21 (r)

Abstract

In this paper, we analyse the proper curve γ(s) lying on the pseudo-sphere. We develop an orthogonal frame {V1, V2, V3 } along the proper curve, lying on pseudosphere. Next, we find the condition for γ(s) to become Vk − slant helix in Minkowski space. Moreover, we find another curve β(¯s) lying on pseudosphere or hyperbolic plane heaving V2 =¯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. © 2022, Hacettepe University. All rights reserved.