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

  • Yasemin SağiroğluEmail author


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.


Dual number Curve Invariant Similarity geometry 

Mathematics Subject Classification

53A35 53A40 53A55 53A99 



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


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Authors and Affiliations

  1. 1.Department of MathematicsKaradeniz Technical UniversityTrabzonTurkey

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