• Title/Summary/Keyword: Lorentz-Minkowski 4-space

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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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SPACE-LIKE COMPLEX HYPERSURFACES OF A COMPLEX LORENTZ MANIFOLD

  • Kwon, Jung-Hwan;Nakagawa, Hisao
    • Bulletin of the Korean Mathematical Society
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    • v.26 no.1
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    • pp.75-82
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    • 1989
  • It is recently proved by Aiyama and the authors [2] that a complete space-like complex submanifold of a complex space form $M^{n+p}$$_{p}$ (c') (c'.geq.0) is to totally geodesic. This is a complex version of the Bernstein-type theorem in the Minkowski space due to Calabi [4] and Cheng and Yau [5], which is generalized by Nishikawa[7] in the Lorentz manifold satisfying the strong energy condition. The purpose of this paper is to consider his result in the complex Lorentz manifold and is to prove the following.e following.

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CANAL HYPERSURFACES GENERATED BY NON-NULL CURVES IN LORENTZ-MINKOWSKI 4-SPACE

  • Mustafa Altin;Ahmet Kazan;Dae Won Yoon
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.5
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    • pp.1299-1320
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    • 2023
  • In the present paper, firstly we obtain the general expression of the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres, pseudo hyperbolic hyperspheres and null hyper-cones whose centers lie on a non-null curve with non-null Frenet vector fields in E41 and give their some geometric invariants such as unit normal vector fields, Gaussian curvatures, mean curvatures and principal curvatures. Also, we give some results about their flatness and minimality conditions and Weingarten canal hypersurfaces. Also, we obtain these characterizations for tubular hypersurfaces in E41 by taking constant radius function and finally, we construct some examples and visualize them with the aid of Mathematica.

A Comparative Study on Gifted Education for Mathematics in Korea and Foreign Countries (한국과 외국의 수학 영재교육에 대한 비교 연구)

  • Han, Gil-Jun
    • Journal for History of Mathematics
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    • v.23 no.4
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    • pp.31-46
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    • 2010
  • Theory of minimal surfaces has always been in the center of differential geometry. The most difficult part in minimal surfaces is how to find meaningful examples. In this paper we survey the history of search for minimal surfaces. We also introduce examples of recently emerging maximal surfaces in the Lorentz-Minkowski space and compare the processes in the search for the minimal and the maximal surfaces.