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On kinematics of semiEuclidean submanifolds on the plane
 in E3 1
"... Abstract. In this study, we obtained an equation of homothetic motion of any smooth semiEuclidean submanifold M on its tangent plane at the contact points, along pole curves which are trajectories of instantaneous rotation centers at the contact points. Also, we gave some remarks for the homothetic ..."
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Abstract. In this study, we obtained an equation of homothetic motion of any smooth semiEuclidean submanifold M on its tangent plane at the contact points, along pole curves which are trajectories of instantaneous rotation centers at the contact points. Also, we gave some remarks for the homothetic motions that are both sliding and rolling at every moment. We establish a surprising relationship between the curvatures of the moving and fixed pole curves.
ON RECTIFYING CURVES AS CENTRODES AND EXTREMAL CURVES IN THE MINKOWSKI 3SPACE
"... Abstract. In this paper, we characterize the spacelike, the timelike and the null rectifying curves in the Minkowski 3space in terms of centrodes. In particular, we show that the spacelike and timelike rectifying curves are the extremal curves for which the corresponding function takes its extremal ..."
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Abstract. In this paper, we characterize the spacelike, the timelike and the null rectifying curves in the Minkowski 3space in terms of centrodes. In particular, we show that the spacelike and timelike rectifying curves are the extremal curves for which the corresponding function takes its extremal value. On the other hand, we also show that the null rectifying curves are not the extremal curves and give some interesting geometric properties of such curves.
c © TÜBİTAK Some Characterizations of Rectifying Curves in the Euclidean Space E4
"... In this paper, we define a rectifying curve in the Euclidean 4space as a curve whose position vector always lies in orthogonal complement N ⊥ of its principal normal vector field N. In particular, we study the rectifying curves in E4 and characterize such curves in terms of their curvature function ..."
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In this paper, we define a rectifying curve in the Euclidean 4space as a curve whose position vector always lies in orthogonal complement N ⊥ of its principal normal vector field N. In particular, we study the rectifying curves in E4 and characterize such curves in terms of their curvature functions. Key Words: Rectifying curve, Frenet equations, curvature. 1.
Normal and Rectifying Curves in PseudoGalilean Space G13 and Their Characterizations
, 2010
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