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    Ball and Burmester points in Lorentzian sphere kinematics
    (Academic Publication Council, 2015) İnalcık, Abdullah; Ersoy, Soley
    In this work, we study Lorentzian spherical motion of rigid bodies by using instantaneous invariants and define Lorentzian inflection curve, Lorentzian circling points curve and Lorentzian cubic of twice stationary curve, which are the loci of points having the same properties during Lorentzian spherical motion of rigid bodies. Also, the intersection points of these curves are called Ball points and Burmester points. We define Lorentzian Ball and Burmester points on Lorentzian sphere.
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    Generalized spacelike bertrand curves in minkowski 5-space R-1(5)
    (Natl Inquiry Services Centre Pty Ltd, 2014) Ersoy, Soley; İnalcık, Abdullah
    In this paper, we give the definition of the generalization of spacelike Bertrand curves and obtain the characterization of these curves in Minkowski 5-space R-1(5). Moreover, we define three types special spacelike Bertrand curves in Minkowski 5-space R-1(5).
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    Non-null helicoidal surfaces as non-null bonnet surfaces
    (Math Soc Serbia-Drustvo Matematicara Srbije, 2016) İnalcık, Abdullah; Ersoy, Soley
    In this study, we obtain an equivalent of the Codazzi-Mainardi equations for spacelike and timelike surfaces in three dimensional Lorentz space R3 1 . Also, we find necessary and sufficient conditions for spacelike and timelike helicoidal surfaces with non-null axis to be Bonnet surfaces.
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    On instantaneous invariants of hyperbolic planes
    (Sage Publications, 2017) İnalcık, Abdullah; Ersoy, Soley; Stachel, Hellmuth
    In this study, we consider the kinematics of the hyperbolic plane and define the notions of inflection curve, circling-point curve, cubic of twice stationary curvature curve, and cubic of thrice stationary curve. We also obtain Cartesian and parametric equations of these curves and illustrate some special cases. Finally, we investigate the hyperbolic Ball point, the ordinary and the sixth-order Burmester points in the case of a finite instant pole.