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

Khadjiev D.

TURKISH JOURNAL OF MATHEMATICS, cilt.34, sa.4, ss.543-559, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 4
  • Basım Tarihi: 2010
  • Doi Numarası: 10.3906/mat-0809-10
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.543-559
  • Karadeniz Teknik Üniversitesi Adresli: Hayır

Özet

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