In this study, we investigate the evolution of a moving space curve with a modified orthogonal frame. Firstly, the relations between the Frenet frame and the modified orthogonal frame is given. Later, the time evolution ...

In this study, we investigate the geometric and algebraic aspects of defocusing Complex Coupled Dispersionless (CCD) equations in Minkowski space. We give the conditions for obtaining CCD equations from moving spacelike ...

In this study, we investigate coupled real and complex dispersionless equations for curve families, even if they have singular points. Even though the connections with the differential equations and regular curves were ...

In this paper, we derive the coupled dispersionless (CD) equation from the motion of the involute evolute curve pairs, which provides a favourable interpretation for the integrability conditions. This nonlinear differential ...

Many curve evolutions have been determined which are integrable in recent times. The motion of curves can be defined by certain integrable equations including the modified Korteweg-de Vries. In this study, the quaternionic ...

In this study, the partner-ruled surfaces in Minkowski 3-space, which are defined according to the Frenet vectors of non-null space curves, are introduced with extra conditions that guarantee the existence of definite ...

Involute-evolute curve pairs enable us to forecast their behaviors in various situations because of their well-defined mathematical characteristics. A mathematical surface connected to the localized induction equation (LIE) ...

Bu tez beş bölümden oluşmaktadır. Birinci bölüm giriş kısmına ayrılmıştır. İkinci bölümde iki ve üç boyutlu Minkowski uzaylarında açı ve vektör kavramları, temel tanımlar ve gerekli teoremler verilmiştir. Üçüncü bölümde ...