ED标架下的类法曲线

doi:10.13438/j.cnki.jdzk.2025.03.004

吉首大学学报（自然科学版） ›› 2025, Vol. 46 ›› Issue (3): 21-29.DOI: 10.13438/j.cnki.jdzk.2025.03.004

ED标架下的类法曲线

胡娜，刘昊燃

（沈阳工业大学理学院，辽宁沈阳 110870）

出版日期:2025-05-25 发布日期:2025-06-12
作者简介:胡娜（1985—），女，辽宁沈阳人，沈阳工业大学理学院副教授，博士研究生，主要从事基础数学研究.
基金资助:
辽宁省教育厅基本科研项目（LJKMZ20220485）

Normal-Like Curves According to the ED-Frame in E41

HU Na,LIU Haoran

（School of Science,Shenyang University of Technology,Shenyang 110870,China）

Online:2025-05-25 Published:2025-06-12

摘要/Abstract

摘要：基于扩展Darboux标架（ED标架），定义了E₄空间中特殊情况的ED标架下的类法曲线.将类法曲线的概念扩展到E₄¹空间，深入分析了类法曲线的特征，推导出超曲面M上与类法曲线曲率有关的3个方程.这些方程是判断E₄¹空间中类法线曲线的充要条件.通过利用ED标架，在E₄¹空间中定义了E的表达式，并给出了应用实例.

关键词： 类法曲线, 扩展Darboux 标架, 曲率, 挠率

Abstract: Based on the extended Darboux (ED)-framework,the normal-like curves under a specific ED-frame in E4 is defined.The concept of normal curves is extended to E41,and the characteristics of normal-like curves are analyzed in depth.Three equations relating the curvature of normal curves on hypersurfaces M are derived.These equations serve as the necessary and sufficient conditions for normal-like curves in E41.By applying the ED-frame,we define the E-expressions in E41 and give concrete application examples.

Key words: normal-like curve, extended Darboux framework, curvature, torsion

胡娜, 刘昊燃. ED标架下的类法曲线[J]. 吉首大学学报（自然科学版）, 2025, 46(3): 21-29.

HU Na, LIU Haoran. Normal-Like Curves According to the ED-Frame in E41[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(3): 21-29.

参考文献

[1] ILARSLAN KAZIM.Spacelike Normal Curves in Minkowski 3-Space[J].Turkish Journal of Mathematics,2005,29(1):53-63.
[2] ILARSLAN KAZIM, NEŠOVIĆ EMILIJA. Spacelike and Timelike Normal Curves in Minkowski Space-Time[J]. Publications de l'Institut Mathématique, 2009(105): 111-118.
[3] GRBOVIĆ MILICA, NEŠOVIĆ EMILIJA. Some Relations Between Rectifying and Normal Curves in Minkowski 3-Space[J]. Mathematical Communications, 2012, 17(2): 655-664.
[4] BEKTA塁 ZCAN.Normal Curves in n-Dimensional Euclidean Space[J].Advances in Difference Equations,2018,2018(1):1-12.
[5] YAZICI BAHAR DOGAN,KARAKUS SIDDIKA OZKALDI,TOSUN MURAT.Framed Normal Curves in Euclidean Space[J].Tbilisi Mathematical Journal,2021,10(1):27-37.
[6] KALKAN ZGUR BOYACIOGLU.On Normal Curves and Their Characterizations in Lorentzian n-Space[J].AIMS Mathematics,2020,5(4):3510-3524.
[7] MOSA SAFAA,El-FAKHARANY MOHAMED,ELZAWY MERVAT.Normal Curves in 4-Dimensional Galilean Space G4[J].Frontiers in Physics,2021,9:660241.DOI:10.3389/fphy.2021.660241.
[8] ISAH MUHAMMAD ABUBAKAR,ISAH IBRAHIM,HASSAN TIJJANI LAWAN,et al.Some Characterization of Osculating Curves According to Darboux Frame in Three Dimensional Euclidean Space[J].International Journal of Advanced Academic Research,2021,7(12):47-56.
[9] KAZAZ MUSTAFA, UĞURLU H. HUSEYIN, ÖNDER MEHMET, et al. Mannheim Partner D-Curves in the Euclidean 3-Space[J]. New Trends in Mathematical Sciences, 2015, 3(2): 24-35.
[10] ALIҪ ŞENAY, YILMAZ BEYHAN. Smarandache Curves According to Alternative Frame in

[J]. Journal of Universal Mathematics, 2021, 4(2): 140-156.
[11] DLDL B U.Some Special Smarandache Curves According to the Extended Darboux Frame in E41[J].Malaya Journal of Matematik,2019,7(1):72-75.
[12] DLDL BAHAR UYAR.Smarandache Curves According to the Extended Darboux Frame in Euclidean 4-Space[M].Journal of Computer Science & Computational Mathematics,2019,9(2):17-22.
[13] BEKTA塁 ZCAN.Normal-Like Curves with Respect to the Special Case of the ED-Frame in Euclidean 4-Space[J].Hagia Sophia Journal of Geometry,2022,4(1):20-24.
[14] KRPINAR TALAT,NLTRK YASIN.An Approach to Energy and Elastic for Curves with Extended Darboux Frame in Minkowski Space[J].AIMS Mathematics,2020,5(2):1025-1034.
[15] KRPINAR TALAT,NLTRK YASIN.A New Approximation for Bienergy and Biangle of Particles with Extended Darboux Frame in Minkowski Spacetime[J].Waves in Random and Complex Media,2022,12(4):1-13.

ED标架下的类法曲线

Normal-Like Curves According to the ED-Frame in E41

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[13]	王敏生, 王庚. 二维常曲率空间中的2个几何不等式[J]. journal6, 2006, 27(5): 4-5.
[14]	肖调生, 阳勇 . 结构损伤识别的柔度差值曲率法[J]. journal6, 2006, 27(2): 74-76.
[15]	吴金文. 常平均曲率曲面的整体性质[J]. journal6, 2001, 22(3): 73-76.