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- 저자 : Melek Erdogdu (검색결과 2 건)
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BETCHOV-DA RIOS EQUATION BY NULL CARTAN, PSEUDO NULL AND PARTIALLY NULL CURVE IN MINKOWSKI SPACETIME
Melek Erdogdu,Yanlin Li,Ayse Yavuz 대한수학회 2023 대한수학회보 Vol.60 No.5
The aim of this paper is to investigate Betchov-Da Rios equation by using null Cartan, pseudo null and partially null curve in Minkowski spacetime. Time derivative formulas of frame of $s$ parameter null Cartan, pseudo null and partially null curve are examined, respectively. By using the obtained derivative formulas, new results are given about the solution of Betchov-Da Rios equation. The differential geometric properties of these solutions are obtained with respect to Lorentzian causal character of $s$ parameter curve. For a solution of Betchov-Da Rios equation, it is seen that null Cartan $s$ parameter curves are space curves in three-dimensional Minkowski space. Then all points of the soliton surface are flat points of the surface for null Cartan and partially null curve. Thus, it is seen from the results obtained that there is no surface corresponding to the solution of Betchov-Da Rios equation by using the pseudo null $s$ parameter curve.
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A GEOMETRIC APPROACH TO TIMELIKE FLOWS IN TERMS OF ANHOLONOMIC COORDINATES
Ays¸e Yavuz,Melek Erdogdu 호남수학회 2022 호남수학학술지 Vol.44 No.2
This paper is devoted to the geometry of vector fields and timelike flows in terms of anholonomic coordinates in three dimensional Lorentzian space. We discuss eight parameters which are related by three partial differential equations. Then, it is seen that the curl of tangent vector field does not include any component in the direction of principal normal vector field. This implies the existence of a surface which contains both s − lines and b − lines. Moreover, we examine a normal congruence of timelike surfaces containing the s − lines and b − lines. Considering the compatibility conditions, we obtain the Gauss-Mainardi-Codazzi equations for this normal congruence of timelike surfaces in the case of the abnormality of normal vector field is zero. Intrinsic geometric properties of these normal congruence of timelike surfaces are obtained. We have dealt with important results on these geometric properties.
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