Browsing by Author "Samanci, HK"

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    Some New Characterizations of The Harmonic and Harmonic 1-Type Curves in Euclidean 3-Space
    Samanci, HK; Ayaz, S; Kocayigit, H
    A Laplace operator and harmonic curve have very important uses in various engineering science such as quantum mechanics, wave propagation, diffusion equation for heat, and fluid flow. Additionally, the differential equation characterizations of the harmonic curves play an important role in estimating the geometric properties of these curves. Hence, this paper proposes to compute some new differential equation characterizations of the harmonic curves in Euclidean 3-space by using an alternative frame named the N-Bishop frame. Firstly, we investigated some new differential equation characterizations of the space curves due to the N-Bishop frame. Secondly, we firstly introduced some new space curves which have the harmonic and harmonic 1-type vectors due to alternative frame N-Bishop frame. Finally, we compute new differential equation characterizations using the N-Bishop Darboux and normal Darboux vectors. Thus, using these differential equation characterizations we have proved in which conditions the curve indicates a helix.
  • No Thumbnail Available
    Item
    N-BISHOP DARBOUX VECTOR OF THE SPACELIKE CURVE WITH SPACELIKE BINORMAL
    Samanci, HK; Kocayigit, H
    In this article, the N-Bishop frame in Minkowski space is investigated for space like curves with a spacelike binormial. Some features of the normal expansion are proven via for the spacelike curve. Then, a new Darboux frame called by the N-Bishop Darboux frame is introduced at first time. Furthermore, some geometrical properties of the N-Bishop Darboux frame are proven. As a result, the N-Bishop Darboux axis and momentum rotation vector are calculated.
  • No Thumbnail Available
    Item
    Some new characterizations of a space curve due to a modified frame {(N)over-right-arrow, (C)over-right-arrow, (W)over-right-arrow} in Euclidean 3-space
    Samanci, HK; Ayaz, S; Kocayigit, H
    In our paper, we computed some new characterizations {(N) over right arrow, (C) over right arrow, (W) over right arrow} in Euclidean 3-space and we get general differential equation characterizations of a space curve due to the vectors.(N) over right arrow, (C) over right arrow, (W) over right arrow . Furthermore, we investigated some differential equations characterizations of the harmonic and harmonic 1-type curves.