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.
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Sağiroğlu, Y. Global Invariants of Paths and Curves in the Two-Dimensional Real Vector Space for Linear Similarity Groups Generated by Dual Numbers. Adv. Appl. Clifford Algebras 29, 10 (2019). https://doi.org/10.1007/s00006-018-0929-9
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DOI: https://doi.org/10.1007/s00006-018-0929-9