• Title/Summary/Keyword: dual Lorentzian space

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THE RELATIONS BETWEEN NULL GEODESIC CURVES AND TIMELIKE RULED SURFACES IN DUAL LORENTZIAN SPACE 𝔻31

  • Unluturk, Yasin;Yilmaz, Suha;Ekici, Cumali
    • Honam Mathematical Journal
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    • v.41 no.1
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    • pp.185-195
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    • 2019
  • In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.

QUATERNIONS AND HOMOTHETIC MOTIONS IN EUCLIDEAN AND LORENTZIAN SPACES

  • Gulsum YUCA;Yusuf YAYLI
    • Honam Mathematical Journal
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    • v.45 no.2
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    • pp.198-214
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    • 2023
  • In the present paper, we investigate homothetic motions determined by quaternions, which is a general form of our previous paper [20]. We introduce a transition between homothetic motions in 3D and 4D Euclidean and Lorentzian spaces. In other words, we give a new method that works as a handy tool for obtaining Lorentzian homothetic motions from Euclidean homothetic motions. Moreover, some remarkable properties of homothetic motions, which are given in former studies on this subject, are also examined by dual transformations. Then, we present applications and visualize them with 3D-plots. Finally, we investigate homothetic motions in dual spaces because of the importance in many fields related to kinematics.

ON THE SCALAR AND DUAL FORMULATIONS OF THE CURVATURE THEORY OF LINE TRAJECTORIES IN THE LORENTZIAN SPACE

  • Ayyildiz, Nihat;Yucesan, Ahmet
    • Journal of the Korean Mathematical Society
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    • v.43 no.6
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    • pp.1339-1355
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    • 2006
  • This paper develops in detail the differential geometry of ruled surfaces from two perspectives, and presents the underlying relations which unite them. Both scalar and dual curvature functions which define the shape of a ruled surface are derived. Explicit formulas are presented for the computation of these functions in both formulations of the differential geometry of ruled surfaces. Also presented is a detailed analysis of the ruled surface which characterizes the shape of a general ruled surface in the same way that osculating circle characterizes locally the shape of a non-null Lorentzian curve.