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

KHADJIEV, Djavvat

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

Djavvat KHADJIEV (Karadeniz Teknik Üniversitesi, Matematik Bölümü, Trabzon, Türkiye)

Turkish Journal of Mathematics

2 0

Yıl: 2010 Cilt: 34 Sayı: 4 Sayfa Aralığı: 543 - 559 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

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

Öz:

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 Rn 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.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	KHADJIEV D (2010). Complete systems of differential invariants of vector fields in a euclidean space. , 543 - 559.
Chicago	KHADJIEV Djavvat Complete systems of differential invariants of vector fields in a euclidean space. (2010): 543 - 559.
MLA	KHADJIEV Djavvat Complete systems of differential invariants of vector fields in a euclidean space. , 2010, ss.543 - 559.
AMA	KHADJIEV D Complete systems of differential invariants of vector fields in a euclidean space. . 2010; 543 - 559.
Vancouver	KHADJIEV D Complete systems of differential invariants of vector fields in a euclidean space. . 2010; 543 - 559.
IEEE	KHADJIEV D "Complete systems of differential invariants of vector fields in a euclidean space." , ss.543 - 559, 2010.
ISNAD	KHADJIEV, Djavvat. "Complete systems of differential invariants of vector fields in a euclidean space". (2010), 543-559.

APA	KHADJIEV D (2010). Complete systems of differential invariants of vector fields in a euclidean space. Turkish Journal of Mathematics, 34(4), 543 - 559.
Chicago	KHADJIEV Djavvat Complete systems of differential invariants of vector fields in a euclidean space. Turkish Journal of Mathematics 34, no.4 (2010): 543 - 559.
MLA	KHADJIEV Djavvat Complete systems of differential invariants of vector fields in a euclidean space. Turkish Journal of Mathematics, vol.34, no.4, 2010, ss.543 - 559.
AMA	KHADJIEV D Complete systems of differential invariants of vector fields in a euclidean space. Turkish Journal of Mathematics. 2010; 34(4): 543 - 559.
Vancouver	KHADJIEV D Complete systems of differential invariants of vector fields in a euclidean space. Turkish Journal of Mathematics. 2010; 34(4): 543 - 559.
IEEE	KHADJIEV D "Complete systems of differential invariants of vector fields in a euclidean space." Turkish Journal of Mathematics, 34, ss.543 - 559, 2010.
ISNAD	KHADJIEV, Djavvat. "Complete systems of differential invariants of vector fields in a euclidean space". Turkish Journal of Mathematics 34/4 (2010), 543-559.