Geometry of Timelike Normal Surfaces in De Sitter 3-Space

Abstract

In this paper, we characterize the normal surfaces of regular curves in de Sitter 3-space, which is a pseudosphere in 4-dimensional Minkowski space. The results obtained in terms of curvatures, which are the basic parameters of curves in differential geometry, have always been meaningful. Here we examine with the help of the given normal surface curvatures associated with a regular curve. First of all, we obtain the geometric components of the surface, such as fundamental forms and curvatures, in terms of the curvatures of the curve. Then, we examine the special conditions of this surface, such as minimalness and flatness. Finally, we obtain some new characterizations, theorems, and results with the help of the obtained equations.