Tubular involutive surfaces with Frenet frame in Euclidean 3-space

Bilici M., Koseoglu G.

Maejo International Journal of Science and Technology, vol.17, no.2, pp.96-106, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 2
  • Publication Date: 2023
  • Journal Name: Maejo International Journal of Science and Technology
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Agricultural & Environmental Science Database, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), CAB Abstracts, Communication Abstracts, Metadex, Veterinary Science Database, Directory of Open Access Journals, Civil Engineering Abstracts
  • Page Numbers: pp.96-106
  • Keywords: Frenet frame, involute curve, singularity, tubular surface
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this study we first define the tubular involutive surfaces as a new surface form. We then investigate singularity, Gaussian curvature and mean curvatures of the tubular involutive surfaces and get an interesting relation between these curvatures as 2H = −(rK + 1/r). By calculating the Gaussian and mean curvatures of the tubular involutive surfaces, we find the necessary conditions of being flat or minimal of these surfaces. In addition, we analyse the necessary and sufficient conditions for parameter curves on the surface to be asymptotic, geodesic and line of curvature. Finally, we illustrate our method by presenting two examples.