HOLDITCH THEOREM FOR THE CLOSED SPACE CURVES IN LORENTZIAN 3-SPACE

In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by us...

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Bibliographic Details
Published in:Acta mathematica scientia 2011, Vol.31 (1), p.172-180
Main Authors: Yildirim, Handan, Yüce, Salim, Kuruoğlu, Nuri
Format: Article
Language:English
Subjects:
53A17
53B30
53B50
Asymptotic properties
Estimates
Holditch Theorem
Infinity
Lorentzian matrix multiplication
Lorentzian motion
Lorentz空间
Mathematical analysis
Multiplication
orthogonal projection area
Planes
Projection
Separation
Theorems
不动点定理
封闭曲线
封闭空间
投影面积
洛仑兹
洛伦兹空间
空间曲线
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Summary:In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(11)60218-X