Browsing by Author "Uǧurlu H.H."

Now showing 1 - 5 of 5
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    Fundamental theorems for the hyperbolic geodesic triangles
    (2005) Uǧurlu H.H.; Kazaz M.; Özdemir A.
    In this work, we state and prove the sine, cosine I, cosine II, sine-cosine and cotangent rules for spherical triangles on the hyperbolic unit sphere H02 in the Lorentzian space R13.
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    The Cosine Rule II for a spherical triangle on the dual unit sphere S̃2
    (2005) Kazaz M.; Uǧurlu H.H.; Özdemir A.
    In this work, we proved the Cosine Rule II for a spherical triangle on the dual unit sphere S̃2. © Association for Scientific Research.
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    Frenet frames and invariants of timelike ruled surfaces
    (Ain Shams University, 2013) Önder M.; Uǧurlu H.H.
    In this study we give the Frenet frames and Frenet invariants of timelike ruled surfaces. We show that a timelike ruled surface and its directing cone have the same base of Frenet frame. We define instantaneous rotation vectors of the Frenet frames of timelike ruled surfaces. Also we prove the Chasles Theorem for timelike ruled surfaces. © 2012 Ain Shams University. Production and hosting by Elsevier B.V. All rights reserved.
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    Blaschke approach to dual Smarandache curves
    (Institute of Advanced Scientific Research, Inc., 2013) Kahraman T.; Önder M.; Uǧurlu H.H.
    In this paper, we give the definition of dual Smarandache curves on dual unit sphere ~S2 according to Blaschke frame. We obtain the relationships between Blaschke frames, invariants and elements of curvature of a dual curve α̃ and its dual Smarandache b̃ij-curves (1 ≤ i, j ≤ 3). Furthermore, we show that a dual curve α̃ and its dual Smarandache b̃13-curve forms a Bertrand offset. © 2013 Institute of Advanced Scientific Research.
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    Normal and Spherical Curves in Dual Space D 3
    (Birkhauser Verlag AG, 2013) Önder M.; Uǧurlu H.H.
    In this paper, we give the definitions and characterizations of normal and spherical curves in the dual space D 3. We show that normal curves are also spherical curves in D 3. © 2013 Springer Basel.