利用扩展Darboux框架场与Betchov-Da Rios方程相关的孤子曲面在E4中的几何应用

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2025-02-01 DOI:10.1016/S0034-4877(25)00011-4

Ahmet Kazan, Mustafa Altin

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引用次数: 0

摘要

本文针对与Betchov-Da Rios方程相关的孤子曲面Ω = Ω（u, v），得到了单位速度u参数曲线Ω = Ω（u, v）对所有v的扩展Darboux坐标系场的导数公式，并得到了孤子曲面Ω = Ω（u, v）的几何不变量k和h，得到了Ω的高斯曲率、平均曲率矢量和高斯扭转。利用这些不变量，给出了平面性、极小性和半脐性等重要的几何特征。此外，我们还研究了扩展Darboux坐标系场下Betchov-Da Rios孤子曲面和Wintgen理想（超共形）Betchov-Da Rios孤子曲面的曲率椭圆。最后，利用扩展的Darboux框架域构造了Betchov-Da Rios孤子曲面的一个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Geometric Application of Soliton Surfaces Associated with The Betchov–Da Rios Equation Using an Extended Darboux Frame Field in E4

In this paper, for a soliton surface Ω = Ω(u, v) associated with the Betchov–Da Rios equation, we obtain the derivative formulae of an extended Darboux frame field of a unit speed u-parameter curve Ω = Ω(u, v) for all v. Also, we get the geometric invariants k and h of the soliton surface Ω = Ω(u, v) and we obtain the Gaussian curvature, mean curvature vector and Gaussian torsion of Ω. We give some important geometric characterizations such as flatness, minimality and semi-umbilicaly with the aid of these invariants. Additionally, we study the curvature ellipse of the Betchov–Da Rios soliton surface and Wintgen ideal (superconformal) Betchov–Da Rios soliton surface with respect to an extended Darboux frame field. Finally, we construct an application for the Betchov–Da Rios soliton surface with the aid of an extended Darboux frame field.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.