A new approach to special curved surface families according to modified orthogonal frame


Talay G.

AIMS MATHEMATICS, vol.9, no.8, pp.20662-20676, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 8
  • Publication Date: 2024
  • Doi Number: 10.3934/math.20241004
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.20662-20676
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

The main purpose of this paper was to investigate the problem of finding the surface family with respect to two different types of modified orthogonal frames defined for curves with curvature and torsion different from zero, respectively. For this purpose, conditions were given for the parametric curve with the modified orthogonal frame in three - dimensional Euclidean space to be a geodesic, asymptotic or line of curvature on the surface, respectively. It has been shown that a member of the surface family with the same special curve such as geodesic, asymptotic, or line of curvature can be obtained by choosing different deviation functions in the parametric writing of the surface to satisfy the conditions. Finally, several examples were given to support the study.