Hypersurface families in 4-dimensional Minkowski space

Prepared as a postgraduate thesis, this study consists of four chapters. In the first chapter, the purpose of the thesis is expressed and information is given about the studies on surface families created by geodesic and asymptotic curves, which have been done before in Euclidean and non Euclidean spaces. In the second chapter, some basic definitions and theorems to be used in oncoming chapters are explained. In the third chapter, parametric equation of surfaces passing through α(s) curve given in 3-dimensional Lorentz-Minkowski space is explained with the help of Frenet frame. Then, surface families with spacelike and timelike common isogeodesic and isoasymptotic curves with non-null Frenet vectors have been generated. Moreover, examples to support the study are included. The fourth chapter forms the original section of the study. Hypersurface families are formed by giving the necessary and sufficient conditions so that spacelike and timelike α(s) curve in 4-dimensional Lorentz-Minkowski space is isogeodesic and isoasymptotic common on hypersurface. Afterwards, the study has been supported with some examples and these surfaces, whose examples have been given, were projected into 3-dimensional space using certain projection methods and their graphs have been drawn.