Browsing by Author "Şahiner B."

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    Relations between a dual unit vector and Frenet vectors of a dual curve
    (University of Kuwait, 2016) Şahiner B.; Önder M.
    In this paper, we generalize the notions of helix and slant helix in dual space in a more general case such as the dual angle between a fixed dual unit vector and Frenet vectors of a dual curve is not constant. We study the motions of the lines corresponding to dual Frenet vectors and dual Frenet instantaneous rotation vector with respect to a fixed line. We obtain some characterizations for such dual curves and show that these characterizations include the definitions and characterizations of dual helix and dual slant helix in some special cases. © 2016, University of Kuwait. All rights reserved.
  • No Thumbnail Available
    Item
    Quaternionic direction curves
    (Kyungpook National University, 2018) Şahiner B.
    In this paper, we define new quaternionic associated curves called quaternionic principal-direction curves and quaternionic principal-donor curves. We give some properties and relationships between Frenet vectors and curvatures of these curves. For spatial quaternionic curves, we give characterizations for quaternionic helices and quaternionic slant helices by means of their associated curves. © Kyungpook Mathematical Journal.
  • No Thumbnail Available
    Item
    Direction curves of tangent indicatrix of a curve
    (Elsevier Inc., 2019) Şahiner B.
    In this paper, we define some new associated curves as integral curves of a vector field generated by Frenet vectors of tangent indicatrix of a curve in Euclidean 3-space. We give some relationships between curvatures of these curves. By using these associated curves, we give some methods to construct helices and slant helices from some special spherical curves such as circles on unit sphere, spherical helices, and spherical slant helices. Finally, we give some related examples. © 2018 Elsevier Inc.