Abstract
In this study, we investigate the rectifying curve and its centrode by using a dilation of a unit speed curve on pseudo-sphere or pseudo-hyperbolic space. Firstly, considering a causal character of any curve, we study the connection between Serret-Frenet apparatus of the curve on pseudo-sphere or pseudo-hyperbolic space and its dilation. Then, we extend necessary conditions in order to make the centrode a rectifying curve. Also, we examine some properties of centrode which is a rectifying curve.
Highlights
Gulsah AYDIN S EKERCI Sibel SEVINCand Abdilkadir Ceylan C O KEN states the axis of instantaneous rotation at each point
We examine some properties of centrode which is a rectifying curve
Deshmukh et al [3] developed the necessary circumstances for the centrode of a curve to be a rectifying curve in Euclidean 3-space and they presented the results about the dilation for rectifying curves and centrodes
Summary
Let α (s) be a curve with an arc-length parameter s It is the non-null curve that satisfies the property g (α (s) , α (s)) = ±1 where is the derivation of α [7]. The rectifying curves are formed by expanding a unit speed curve on a unit sphere with a special factor f To characterize such rectifying curves in E31, ̇Ilarslan et al [5] gave a theorem. A unit speed non-null curve α = α (s) is written as the dilation of the curve u (t) to be rectifying curve It is a rectifying curve with a spacelike rectifying plane if and only if it satisfies the condition l α (t) = u (t).
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