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


Khadjiev D.

TURKISH JOURNAL OF MATHEMATICS, cilt.34, ss.543-559, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 34 Konu: 4
  • Basım Tarihi: 2010
  • Doi Numarası: 10.3906/mat-0809-10
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.543-559

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