Yazar "Li, Yanlin" seçeneğine göre listele

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    BETCHOV-DA RIOS EQUATION BY NULL CARTAN, PSEUDO NULL AND PARTIALLY NULL CURVE IN MINKOWSKI SPACETIME
    (Korean Mathematical Soc, 2023) Erdogdu, Melek; Li, Yanlin; Yavuz, Ayse
    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 geomet-ric 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 sur-face 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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    Differential geometric approach of Betchov-Da Rios soliton equation
    (Hacettepe University Faculty of Science, 2023) Li, Yanlin; Erdoğdu, Melek; Yavuz, Ayşe
    In the present paper, we investigate differential geometric properties the soliton surface M associated with Betchov-Da Rios equation. Then, we give derivative formulas of Frenet frame of unit speed curve 4) = 4)(s, t) for all t. Also, we discuss the linear map of Weingarten type in the tangent space of the surface that generates two invariants: k and h. Moreover, we obtain the necessary and sufficient conditions for the soliton surface associated with Betchov-Da Rios equation to be a minimal surface. Finally, we examine a soliton surface associated with Betchov-Da Rios equation as an application. Mathematics Subject Classification (2020). 35Q55, 53A05
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    Evolving evolutoids and pedaloids from viewpoints of envelope and singularity theory in Minkowski plane
    (Elsevier, 2022) Yang, Zhichao; Li, Yanlin; Erdogdu, Melek; Zhu, Yushu
    In this paper, we take advantage of envelope theory and singularity theory to study the evolutoids and pedaloids in Minkowski plane. We illustrate an internal correlation from algebraic and geometric viewpoints, and give the geometric explanation of evolutoids and pedaloids. Then, we generalize the notions of evolutoids and pedaloids to the category of frontals in Minkowski plane. Furthermore, we apply the technique of singularity theory, using the discriminants and versal unfolding tools, to consider evolving evolutoids and give the classifications of singularities of the evolutoids, and explain when cusps and inflexions occur and how evolutoids evolving. Besides, we found that there is a close relationship between the evolutoids and pedaloids and good correspondence between their singularities.(c) 2022 Elsevier B.V. All rights reserved.
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    NONNULL SOLITON SURFACE ASSOCIATED WITH THE BETCHOV-DA RIOS EQUATION
    (Pergamon-Elsevier Science Ltd, 2022) Li, Yanlin; Erdogdu, Melek; Yavuz, Ayse
    The aim of this paper is to investigate the nonnull soliton surfaces associated with Betchov-Da Rios equation in Minkowski space-time. The differential geometric properties of these kind of nonnull soliton surfaces are examined with respect to the Lorentzian casual characterizations. Moreover, the linear maps of Weingarten type are obtained which are defined on tangent spaces of these soliton surfaces. Some new results are obtained by means of two geometric invariants ?? and h which are generated by linear maps of Weingarten type. Then, the mean curvature vector field and Gaussian curvature of the nonnull soliton surface are obtained. Finally, it is shown that this kind of soliton surface consists of flat points as a numerical example.
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    SURFACES WITH VANISHING ABNORMALITY OF NORMAL DIRECTION IN MINKOWSKI SPACE
    (Editura Bibliotheca-Bibliotheca Publ House, 2022) Li, Yanlin; Yavuz, Ayse; Erdogdu, Melek
    This paper is investigated geometry of vector fields along spacelike curve with timelike normal vector by using anholonomic coordinates. Derivative formulas of Frenet Serret frame of the curve are stated which includes eight parameters. Surfaces with vanishing abnormality of normal direction in Minkowski space are examined. Intrinsic geometric properties of these spacelike surfaces are investigated. Finally, the relations between spacelike surfaces with vanishing abnormality of normal direction and NLS, Heisenberg spin equation are investigated as applications.