## SPACELIKE RULED SURFACES IN DE-SITTER 3-SPACE

Published: 2021-02-25

Page: 37-53

TUGBA MERT *

Department of Mathematics, Faculty of Science, Sivas Cumhuriyet University, 58140, Sivas, Turkey

MEHMET ATC¸ EKEN

Department of Mathematics, Faculty of Science and Arts, Aksaray University, 68100, Aksaray, Turkey.

*Author to whom correspondence should be addressed.

### Abstract

Aims: In this paper, spacelike ruled surfaces are studied in de-Sitter space S13. A ruled surface
in the de-Sitter space S13 is obtained by moving a geodesic along a curve. Developable ruled
surface, striction point, striction curve, dispersion parameter, and orthogonal trajectory concepts
are investigated for the obtained ruled surface. An equivalent condition is provided by means of
the 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 different
spaces related to this subject. The study was completed in Cumhuriyet University and Aksaray
University. From January 2020 to September 2020.
Metho dology: Using the studies of ruled surfaces in different spaces in the literature, the correspondence of such surfaces in de-Sitter space is given.
Results: Developable ruled surface, striction point, striction curve, dispersion parameter, and
orthogonal trajectory concepts are investigated for the obtained ruled surface. An equivalent
condition 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 the
Minkowski space. This study has been prepared to contribute to making more detailed studies on
ruled surfaces. In the first two section, a summary of the literature, basic definitions and theorems
are given for a better understanding of the subject. In the following sections, spacelike ruled surfaces
are defined and examined in detail. As a result, this study has been presented to the literature as
a resource that will be used by every scientist who will study surfaces in the de-Sitter 3-space.

Keywords: Straight geodesic, base curve, striction point, striction curve, de-Sitter Space.

#### How to Cite

MERT, T., & EKEN, M. A. (2021). SPACELIKE RULED SURFACES IN DE-SITTER 3-SPACE. Asian Journal of Mathematics and Computer Research, 27(4), 37–53. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/5974