• Title, Summary, Keyword: Minkowski 3-space

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HELICOIDAL SURFACES AND THEIR GAUSS MAP IN MINKOWSKI 3-SPACE

  • Choi, Mie-Kyung;Kim, Young-Ho;Liu, Huili;Yoon, Dae-Won
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.4
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    • pp.859-881
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    • 2010
  • The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.

HELICOIDAL SURFACES OF THE THIRD FUNDAMENTAL FORM IN MINKOWSKI 3-SPACE

  • CHOI, MIEKYUNG;YOON, DAE WON
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1569-1578
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    • 2015
  • We study helicoidal surfaces with the non-degenerate third fundamental form in Minkowski 3-space. In particular, we mainly focus on the study of helicoidal surfaces with light-like axis in Minkowski 3-space. As a result, we classify helicoidal surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form on the surface.

CURVE COUPLES AND SPACELIKE FRENET PLANES IN MINKOWSKI 3-SPACE

  • Ucum, Ali;Ilarslan, Kazim;Karakus, Siddika Ozkaldi
    • Honam Mathematical Journal
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    • v.36 no.3
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    • pp.475-492
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    • 2014
  • In this study, we have investigated the possibility of whether any spacelike Frenet plane of a given space curve in Minkowski 3-space $\mathbb{E}_1^3$ also is any spacelike Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

GEOMETRIC CHARACTERIZATIONS OF CANAL SURFACES IN MINKOWSKI 3-SPACE I

  • Fu, Xueshan;Jung, Seoung Dal;Qian, Jinhua;Su, Mengfei
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.4
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    • pp.867-883
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    • 2019
  • The canal surfaces foliated by pseudo spheres $\mathbb{S}_1^2$ along a space curve in Minkowski 3-space are studied. The geometric properties of such surfaces are shown by classifying the linear Weingarten canal surfaces, the developable, minimal and umbilical canal surfaces are discussed at the same time.

ON TIMELIKE BERTRAND CURVES IN MINKOWSKI 3-SPACE

  • Ucum, Ali;Ilarslan, Kazim
    • Honam Mathematical Journal
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    • v.38 no.3
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    • pp.467-477
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    • 2016
  • In this paper, we study the timelike Bertrand curves in Minkowski 3-space. Since the principal normal vector of a timelike curve is spacelike, the Bertrand mate curve of this curve can be a timelike curve, a spacelike curve with spacelike principal normal or a Cartan null curve, respectively. Thus, by considering these three cases, we get the necessary and sufficient conditions for a timelike curve to be a Bertrand curve. Also we give the related examples.

Classification of Ruled Surfaces with Non-degenerate Second Fundamental Forms in Lorentz-Minkowski 3-Spaces

  • Jung, Sunmi;Kim, Young Ho;Yoon, Dae Won
    • Kyungpook Mathematical Journal
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    • v.47 no.4
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    • pp.579-593
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    • 2007
  • In this paper, we study some properties of ruled surfaces in a three-dimensional Lorentz-Minkowski space related to their Gaussian curvature, the second Gaussian curvature and the mean curvature. Furthermore, we examine the ruled surfaces in a three-dimensional Lorentz-Minkowski space satisfying the Jacobi condition formed with those curvatures, which are called the II-W and the II-G ruled surfaces and give a classification of such ruled surfaces in a three-dimensional Lorentz-Minkowski space.

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DIRECTIONAL ASSOCIATED CURVES OF A NULL CURVE IN MINKOWSKI 3-SPACE

  • Qian, Jinhua;Kim, Young Ho
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.1
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    • pp.183-200
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    • 2015
  • In this paper, we define the directional associated curve and the self-associated curve of a null curve in Minkowski 3-space. We study the properties and relations between the null curve, its directional associated curve and its self-associated curve. At the same time, by solving certain differential equations, we get the explicit representations of some null curves.