• Title/Summary/Keyword: Mannheim curve

Search Result 5, Processing Time 0.016 seconds

MANNHEIM PARTNER P-TRAJECTORIES IN THE EUCLIDEAN 3-SPACE E3

  • Isbilir, Zehra;Ozen, Kahraman Esen;Tosun, Murat
    • Honam Mathematical Journal
    • /
    • v.44 no.3
    • /
    • pp.419-431
    • /
    • 2022
  • Mannheim introduced the concept of a pair of curves, called as Mannheim partner curves, in 1878. Until now, Mannheim partner curves have been studied widely in the literature. In this study, we take into account of this concept according to Positional Adapted Frame (PAF) for the particles moving in the 3-dimensional Euclidean space. We introduce a new type special trajectory pairs which are called Mannheim partner P-trajectories in the Euclidean 3-space. The relationships between the PAF elements of this pair are investigated. Also, the relations between the Serret-Frenet basis vectors of Mannheim partner P-trajectories are given. Afterwards, we obtain the necessary conditions for one of these trajectories to be an osculating curve and for other to be a rectifying curve. Moreover, we provide an example including an illustrative figure.

A NEW APPROACH FOR CHARACTERIZATION OF CURVE COUPLES IN EUCLIDEAN 3-SPACE

  • Karakus, Siddika Ozkaldi;Ilarslan, Kazim;Yayli, Yusuf
    • Honam Mathematical Journal
    • /
    • v.36 no.1
    • /
    • pp.113-129
    • /
    • 2014
  • In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space $\mathbb{E}_3$ also is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

ON ADJOINT CURVES OF FRAMED CURVES AND SOME RULED SURFACES

  • Bahar Dogan Yazici;Siddika Ozkaldi Karakus;Murat Tosun
    • Honam Mathematical Journal
    • /
    • v.45 no.3
    • /
    • pp.380-396
    • /
    • 2023
  • In this study, we introduce the adjoint curves of framed curves. We examine some characterizations of adjoint curve of a framed curve. In addition, we give the conditions for framed curves and adjoint curves to be Bertrand and Mannheim curves. Then, we introduce adjoint curves of Frenet-type framed curves and give ruled surfaces related to adjoint curves. Finally, we create normal and binormal surfaces of the framed adjoint curves and obtain some characterizations of these surfaces and we support by the results with figures.

CURVE COUPLES AND SPACELIKE FRENET PLANES IN MINKOWSKI 3-SPACE

  • Ucum, Ali;Ilarslan, Kazim;Karakus, Siddika Ozkaldi
    • Honam Mathematical Journal
    • /
    • v.36 no.3
    • /
    • pp.475-492
    • /
    • 2014
  • In this study, we have investigated the possibility of whether any spacelike Frenet plane of a given space curve in Minkowski 3-space $\mathbb{E}_1^3$ also is any spacelike Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.