SPACELIKE RULED SURFACES IN DE-SITTER 3-SPACE

Aims:In this paper, spacelike ruled surfaces are studied in de-Sitter spaceS31.A ruled surfacein the de-Sitter spaceS31is obtained by moving a geodesic along a curve. Developable ruledsurface, striction point, striction curve, dispersion parameter, and orthogonal trajectory conceptsare investigated for the obtained ruled surface. An equivalent condition is provided by means ofthe dispersion parameter for the developable ruled surfaces.Study Design:Cross-sectional study.Place and Duration of Study:The data for this study were collected from studies in differentspaces related to this subject. The study was completed in Cumhuriyet University and AksarayUniversity. From January 2020 to September 2020.Methodology:Using the studies of ruled surfaces in different spaces in the literature, the correspon-dence of such surfaces in de-Sitter space is given.Results:Developable ruled surface, striction point, striction curve, dispersion parameter, andorthogonal trajectory concepts are investigated for the obtained ruled surface. An equivalentcondition is provided by means of the dispersion parameter for the developable ruled surfaces.Conclusion:For many years, many studies have been done on the geometry of surfaces in theMinkowski space. This study has been prepared to contribute to making more detailed studies onruled surfaces. In the first two section, a summary of the literature, basic definitions and theoremsare given for a better understanding of the subject. In the following sections, spacelike ruled surfacesare defined and examined in detail. As a result, this study has been presented to the literature asa resource that will be used by every scientist who will study surfaces in the de-Sitter 3-space.