Geodesic
On the connection of geometric properties of curves and properties of their motion groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 227-233

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Connections between geometric properties of curves and properties of their motion groups are established. Motions of two types, namely, positive and negative motions, are defined for curves. A necessary and sufficient condition for a smooth curve to possess a motion of one of these types is given. The notion of a motion group of a curve is defined in different ways, and classes of curves are specified for which these notions coincide. Closed curves are investigated in terms of their motion groups, and a necessary and sufficient condition for a smooth curve to be closed is presented.
Keywords: curve, image of a curve, curvatures of a curve, closedness of a curve.
Mots-clés : motion, group of motions 
E. A. Rogozinnikov. On the connection of geometric properties of curves and properties of their motion groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 227-233. http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a24/
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