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Global Invariants of Paths and Curves in the Two-Dimensional Real Vector Space for Linear Similarity Groups Generated by Dual Numbers

  • Yasemin Sağiroğlu
Article
  • 12 Downloads

Abstract

Let \(\mathbb {D}\) be the algebra of dual numbers and \(G=M^{+}(\mathbb {D^{*}}), M(\mathbb {D^{*}})\) be linear similarity groups generated by the algebra \(\mathbb {D}\) in two-dimensional real vector space \(R^{2}\). The present paper is devoted to solutions of problems of global G-equivalence of paths and curves in \(R^{2}\) for groups \(G=M^{+}(\mathbb {D^{*}}), M(\mathbb {D^{*}})\). Complete systems of global G-invariants of a path and a curve in \(R^{2}\) are obtained. Existence and uniqueness theorems are given. Evident forms of a path and a curve with the given complete system of G-invariants are obtained.

Keywords

Dual number Curve Invariant Similarity geometry 

Mathematics Subject Classification

53A35 53A40 53A55 53A99 

Notes

Acknowledgements

The author is very grateful to the reviewer(s) for helpful comments and valuable suggestions.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsKaradeniz Technical UniversityTrabzonTurkey

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