On Backlund transformation and motion of null Cartan curves
Küçük Resim Yok
Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
World Scientific Publ Co Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The main scope of this paper is to examine null Cartan curves especially the ones with constant torsion. In accordance with this scope, the position vector of a null Cartan curve is stated by a linear combination of the vector fields of its pseudo-orthogonal frame with differentiable functions. However, the most important difference that distinguishes this study from the other studies is that the Bertrand curve couples (timelike, spacelike or null) of null Cartan curves are also examined. Consequently, it is seen that all kinds of Bertrand couples of a given null Cartan curve with constant curvature functions have also constant curvature functions. This result is the most valuable result of the study, but allows us to introduce a transformation on null Cartan curves. Then, it is proved that aforesaid transformation is a Backlund transformation which is well recognized in modern physics. Moreover, motion of an inextensible null Cartan curve is investigated. By considering time evolution of null Cartan curve, the angular momentum vector is examined. And three different situations are given depending on the character of the angular momentum vector Omega. In the case of tau(t) = 0, we discuss the solution of the system which is obtained by compatibility conditions. Finally, we provide the relation between torsion of the curve and the velocity vector components of the moving curve C.
Açıklama
Anahtar Kelimeler
Null Cartan Curve, Backlund Transformation, Bertrand Curve, Motion Of Inextensible Null Cartan Curve
Kaynak
International Journal Of Geometric Methods In Modern Physics
WoS Q Değeri
Q2
Scopus Q Değeri
Q3
Cilt
19
Sayı
1
