Global invariants of paths and curves for the group of all linear similarities in the two-dimensional Euclidean space

Khadjiev D., ÖREN İ., PEKŞEN Ö.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.15, no.6, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 6
  • Publication Date: 2018
  • Doi Number: 10.1142/s0219887818500925
  • Journal Name: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Curve, invariant, similarity, Euclidean geometry, similarity geometry, INTEGRABLE EQUATIONS, PLANE-CURVES, GROUP MODEL, SYSTEMS, MOTIONS, GEOMETRY
  • Karadeniz Technical University Affiliated: Yes

Abstract

K Let E-2 be the 2-dimensional Euclidean space, LSim(2) be the group of all linear similarities of E-2 and LSim(+)(2) be the group of all orientation-preserving linear similarities of E-2. The present paper is devoted to solutions of problems of global G-equivalence of paths and curves in E-2 for the groups G = LSim(2), LSim(+)(2). Complete systems of global G-invariants of a path and a curve in E-2 are obtained. Existence and uniqueness theorems are given. Evident forms of a path and a curve with the given global invariants are obtained.