Complete systems of differential invariants of vector fields in a euclidean space

Khadjiev D.

TURKISH JOURNAL OF MATHEMATICS, vol.34, no.4, pp.543-559, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.3906/mat-0809-10
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.543-559
  • Karadeniz Technical University Affiliated: No

Abstract

The system of generators of the differential field of all G-invariant differential rational functions of a vector field in the n-dimensional Euclidean space R(n) is described for groups G = M(n) and G = SM(n), where M(n) is the group of all isometries of R(n) and SM(n) is the group of all euclidean motions of R(n) Using these results, vector field analogues of the first part of the Bonnet theorem for groups Aff(n), M(n), SM(n) in R(n) are obtained, where Aff(n) is the group of all affine transformations of R(n) These analogues are given in terms of the first fundamental form and Christoffel symbols of a vector field