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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Volume 16, Number 3, Pages 227–233 (Mi timm595)  
This article is cited in 1 scientific paper (total in 1 paper)

On the connection of geometric properties of curves and properties of their motion groups

E. A. Rogozinnikov

Ural State University
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Abstract: 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, motion, group of motions, curvatures of a curve, closedness of a curve.
Received: 10.12.2008
Bibliographic databases:
Document Type: Article
UDC: 514.75
Language: Russian
Citation: E. A. Rogozinnikov, “On the connection of geometric properties of curves and properties of their motion groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 3, 2010, 227–233
Citation in format AMSBIB
\Bibitem{Rog10}
\by E.~A.~Rogozinnikov
\paper On the connection of geometric properties of curves and properties of their motion groups
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 3
\pages 227--233
\mathnet{http://mi.mathnet.ru/timm595}
\elib{https://elibrary.ru/item.asp?id=15173483}
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  • https://www.mathnet.ru/eng/timm/v16/i3/p227
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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