Global invariants of paths and curves for the group of all linear similarities in the two-dimensional Euclidean space
Djavvat KhadjievAcademy of Sciences of Uzbekistan, Institute of Mathematics, Tashkent 100125, Uzbekistanİdri̇s ÖrenDepartment of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon 61080, TurkeyÖmer PekşenDepartment of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon 61080, Turkey
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Аннотация
Let [Formula: see text] be the [Formula: see text]-dimensional Euclidean space, [Formula: see text] be the group of all linear similarities of [Formula: see text] and [Formula: see text] be the group of all orientation-preserving linear similarities of [Formula: see text]. The present paper is devoted to solutions of problems of global [Formula: see text]-equivalence of paths and curves in [Formula: see text] for the groups [Formula: see text]. Complete systems of global [Formula: see text]-invariants of a path and a curve in [Formula: see text] are obtained. Existence and uniqueness theorems are given. Evident forms of a path and a curve with the given global invariants are obtained.
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