Browsing by Author "Uğurlu H.H."

Now showing 1 - 4 of 4
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    Disteli Diagram of Dual Hyperbolic Spherical Motion in Dual Lorentzian Space
    (National Academy of Sciences India, 2014) Ekinci Z.; Uğurlu H.H.
    In this paper Disteli diagram is introduced for hyperbolic spatial motion by considering the E. Study mapping of timelike lines. Disteli’s diagram of pure rotations is obtained on a circle of Lorentzian space and also given for the general case. The distribution parameters of the axodes are obtained in Disteli’s diagram. © 2014, The National Academy of Sciences, India.
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    On the Developable Mannheim Offsets of Timelike Ruled Surfaces
    (National Academy of Sciences India, 2014) Önder M.; Uğurlu H.H.
    In this paper, using the classifications of timelike and spacelike ruled surfaces, we study the Mannheim offsets of timelike ruled surfaces in the Minkowski 3-space. First, we define the Mannheim offsets of a timelike ruled surface by considering the Lorentzian casual character of the offset surface. We obtain that the Lorentzian casual character of the Mannheim offset of a timelike ruled surface may be timelike or spacelike. Furthermore, we give characterizations for developable Mannheim offsets of a timelike ruled surface. © 2014, The National Academy of Sciences, India.
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    On the Developable Mannheim Offsets of Spacelike Ruled Surfaces
    (Springer International Publishing, 2017) Önder M.; Uğurlu H.H.
    In this paper, using the classifications of timelike and spacelike ruled surfaces, we define and study the Mannheim offsets of spacelike ruled surfaces in Minkowski 3-space. We give the conditions for offset surfaces to be developable. © 2017, Shiraz University.
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    Characterization of Dual Spacelike Curves on Dual Lightlike Cone (Formula Presented). Utilizing the Structure Function
    (Multidisciplinary Digital Publishing Institute (MDPI), 2024) Balkı Okullu P.; Uğurlu H.H.
    This study is about the dual spacelike curves lying on the dual lightlike cone, which can be either symmetric or asymmetric. We first establish the dual associated curve, which is related to the reference curve. Using these curves and the derivative of the reference curve, we derive the dual asymptotic orthonormal frame. Next, we define the dual structure function, curvature function, and Frenet formulae, and express the curvature function in terms of the dual structure function. This leads to a differential equation that characterizes the dual cone curve in relation to its curvature function. Since curves with constant curvature maintain the same curvature at every point, their geometry is more predictable. Therefore, we assume that the dual cone curvature function is constant and examine how this condition affects the behavior and geometric properties of the dual curves. As a result of this investigation, some new results and definitions are obtained. © 2024 by the authors.