On the sectional curvature of generalized ruled surfaces in n-dimensional Minkowski space, Ir_1^n

Key words: Minkowski space, Ruled surface, Sectional curvature, Lorentzian Beltrami-Euler formula, Lorentzian Beltrami-Meusnier formula, generalized Lamarle formula. This thesis consists of five chapters. First chapter is devoted to the introduction. In the second chapter, Minkowski space, the concept of the angle and vectors in Minkowski space are introduced. Moreover, basic definitions and necessary theorems which are related to semi-Riemannian manifolds and curvatures are given. Third chapter is arranged as two subsections. In this chapter, generalized timelike ruled surface with spacelike generating surface in n ? dimensional Minkowski and generalized timelike ruled surface with timelike generating surface in n ? dimensional Minkowski are summarized. Fourth chapter is the original part of the study and it is organized as two subsections. In the first part, the sectional curvatures of generalized timelike ruled surface with spacelike generating space in the n ? dimensional Minkowski space, 1 n IR are studied and Lorentzian Beltrami-Euler formula, generalized Lorentzian Lamarle formula and I., II., III. type Lorentzian Beltrami-Meusnier formula are obtained for sectional curvature of generalized timelike ruled surface with spacelike generating space. In the second part, the sectional curvatures of generalized timelike ruled surface with timelike generating space in the n ? dimensional Minkowski space, 1 n IR are investigated and I., II., III. and IV. type Lorentzian Beltrami-Euler formula, generalized Lorentzian Lamarle formula and I., II., III. type Lorentzian Beltrami- Meusnier formula are established for sectional curvature of generalized timelike ruled surface with timelike generating space. In fifth chapter of this thesis, a brief summary of the study is given and a suggestion is proposed for investigations on the realm of sectional curvature of ruled surface.