177
Views
75
CrossRef citations to date
0
Altmetric
NOTES

When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane?

Pages 147-152 | Published online: 01 Feb 2018

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (1)

Ali Uçum, Makoto Sakaki & Kazim İlarslan. (2017) On osculating, normal and rectifying bi-null curves in ℝ63. Journal of Dynamical Systems and Geometric Theories 15:1, pages 1-13.
Read now

Articles from other publishers (74)

Alexander Navarro & Yun Myung Oh. (2024) Extending natural mates in Euclidean 3-space and applications to Bertrand pairs. International Electronic Journal of Geometry.
Crossref
Milica Grbović ćirić, Jelena Djordjević & Emilija Nesovic. (2024) On null Cartan rectifying isophotic and rectifying silhouette curves lying on a timelike surface in Minkowski space E^3_1. International Electronic Journal of Geometry.
Crossref
Filiz Ertem Kaya & Süleyman Şenyurt. (2024) Curve-Surface Pairs on Embedded Surfaces and Involute D-Scroll of the Curve-Surface Pair in E3. Symmetry 16:3, pages 323.
Crossref
Huili Liu & Yixuan Liu. (2024) Partner Curves in Three Dimensional Degenerated Space Form. International Electronic Journal of Geometry, pages 213-220.
Crossref
M. Khalifa Saad. (2024) Geometrical Analysis of Spacelike and Timelike Rectifying Curves and their Applications. SSRN Electronic Journal.
Crossref
Pascual Lucas & José Antonio Ortega-Yagües. (2023) Concircular Hypersurfaces and Concircular Helices in Space Forms. Mediterranean Journal of Mathematics 20:6.
Crossref
Kadri Arslan, Betül Bulca & Eray Demirbaş. (2023) On constant-ratio surfaces of rotation in Euclidean 4-space. Asian-European Journal of Mathematics 16:11.
Crossref
M. Elzawy & S. Mosa. (2023) Equiform rectifying curves in Galilean space . Scientific African 22, pages e01931.
Crossref
Zehra İŞBİLİR & Murat TOSUN. (2023) A New Insight on Rectifying-Type Curves in Euclidean 4-Space. International Electronic Journal of Geometry 16:2, pages 644-652.
Crossref
Yanlin Li & Mahmut Mak. (2023) Framed Natural Mates of Framed Curves in Euclidean 3-Space. Mathematics 11:16, pages 3571.
Crossref
Pascual LUCAS & José Antonio ORTEGA YAGÜES. (2023) Concircular helices and concircular surfaces in Euclidean 3-space $\mathbb{R}^{3}$. Hacettepe Journal of Mathematics and Statistics 52:4, pages 995-1005.
Crossref
Areej A. Almoneef & Rashad A. Abdel-Baky. (2023) Some Characteristic Properties of Non-Null Curves in Minkowski 3-Space 𝔼13. Mathematics 11:13, pages 2885.
Crossref
Takeshi Takahashi. (2022) Characterizing the developable surfaces with curves whose position vectors lie in the planes spanned by Darboux frame. Indian Journal of Pure and Applied Mathematics 54:2, pages 456-466.
Crossref
Azeb Alghanemi & Meraj Ali Khan. (2023) Position Vectors of the Natural Mate and Conjugate of a Space Curve. Advances in Mathematical Physics 2023, pages 1-5.
Crossref
Zehra İŞBİLİR, Kahraman Esen ÖZEN & Mehmet GÜNER. (2023) Spinor Representations of Positional Adapted Frame in the Euclidean 3-Space. International Electronic Journal of Geometry 16:1, pages 62-72.
Crossref
Talat Korpinar, Rıdvan DemirkolCemCem & Zeliha Korpinar. (2023) Anholonomic surfaces via directional motion of curves. Filomat 37:6, pages 1777-1792.
Crossref
Luiz C. B. Da Silva. (2022) Characterization of spherical and plane curves using rotation minimizing frames. Boletim da Sociedade Paranaense de Matemática 41, pages 1-6.
Crossref
Bahar Doğan Yazıcı, Sıddıka Özkaldı Karakuş & Murat Tosun. (2021) On the classification of framed rectifying curves in Euclidean space. Mathematical Methods in the Applied Sciences 45:18, pages 12089-12098.
Crossref
Buddhadev PAL & Santosh KUMAR. (2022) Characterization of proper curves and proper helix lying on $S_{1}^2(r)$. Hacettepe Journal of Mathematics and Statistics 51:5, pages 1288-1303.
Crossref
Jiakun Jiang, Siyao Liu, Zhigang Wang & Haiming Liu. (2022) Lorentz–Darboux rectifying surfaces and osculating surfaces along frontal curves on timelike surfaces. International Journal of Geometric Methods in Modern Physics 19:08.
Crossref
Ayşe Yavuz. (2022) A Dynamical Approach to Position Vector of Timelike Curve by Vectorial Momentum, Torque and Tangential Dual Curve. Journal of Nonlinear Mathematical Physics 29:4, pages 818-842.
Crossref
Zehra OZDEMİR, Fatma ATES & Nejat EKMEKÇİ. (2022) Finslerian Viewpoint to the Rectifying, Normal, and Osculating Curves. International Electronic Journal of Geometry 15:1, pages 30-38.
Crossref
Bahar DOĞAN YAZICI, Sıddıka ÖZKALDI KARAKUŞ & Murat TOSUN. (2022) Framed Curves and Their Applications Based on a New Differential Equation. International Electronic Journal of Geometry 15:1, pages 47-56.
Crossref
Beyhan YILMAZ, İsmail GÖK & Yusuf YAYLI. (2022) Differential Equations of Rectifying Curves and Focal Curves in $\mathbb{E}^{n}$. Journal of Mathematical Sciences and Modelling 5:1, pages 8-15.
Crossref
Na Hu, Tingting Zhang & Yang Jiang. (2022) Darboux Vector in Four-Dimensional Space-Time. Advances in Mathematical Physics 2022, pages 1-9.
Crossref
Bahar ABALI & Ahmet YÜCESAN. (2022) Associated curves of a Frenet curve in the dual Lorentzian space. Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71:1, pages 285-304.
Crossref
Özcan BEKTAŞ & Zafer BEKİRYAZICI. (2022) Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space. Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71:1, pages 212-225.
Crossref
Yılmaz Tunçer. (2021) A Different View on Dynamics of Space Curves Geometry. Journal of Nonlinear Mathematical Physics 29:1, pages 73-94.
Crossref
Absos ShaikhAliAli & Pinaki GhoshRanjanRanjan. (2022) On the position vector of surface curves in the Euclidean space. Publications de l'Institut Mathematique Publications de l'Institut Math?matique (Belgrade) 112:126, pages 95-101.
Crossref
Aykut Has, Beyhan Yılmaz, Abdullah Akkurt & Hüseyin Yıldırım. (2022) Conformable special curves in Euclidean 3-space. Filomat 36:14, pages 4687-4698.
Crossref
Absos Ali Shaikh, Young Ho Kim & Pinaki Ranjan Ghosh. (2022) Some characterizations of rectifying and osculating curves on a smooth immersed surface. Journal of Geometry and Physics 171, pages 104387.
Crossref
Jianguo Sun, Yanping Zhao & Xiaoyan Jiang. (2021) On the Geometrical Properties of the Lightlike Rectifying Curves and the Centrodes. Mathematics 9:23, pages 3103.
Crossref
Mahmut AKYİĞİT & Önder Gökmen YILDIZ. (2021) On the Framed Normal Curves in Euclidean 4-space. Fundamental Journal of Mathematics and Applications 4:4, pages 258-263.
Crossref
Çetin Camci, Bang-Yen Chen, Kazım İlarslan & Ali Uçum. (2021) Sequential natural mates of Frenet curves in Euclidean 3-space. Journal of Geometry 112:3.
Crossref
Marilena Jianu, Sever Achimescu, Leonard Dăuş, Adela Mihai, Olimpia-Alice Roman & Daniel Tudor. (2021) Characterization of Rectifying Curves by Their Involutes and Evolutes. Mathematics 9:23, pages 3077.
Crossref
Zafar IQBAL & Joydeep SENGUPTA. (2021) A Study on $f$-Rectifying Curves in Euclidean $n$-Space. Universal Journal of Mathematics and Applications 4:3, pages 107-113.
Crossref
Zafar Iqbal & Joydeep Sengupta. (2021) On f-rectifying curves in the Euclidean 4-space. Acta Universitatis Sapientiae, Mathematica 13:1, pages 192-208.
Crossref
Takeshi Takahashi. (2020) Curves always lie in the plane spanned by Darboux frame. Rendiconti del Circolo Matematico di Palermo Series 2 70:2, pages 1083-1098.
Crossref
Mahmut MAK. (2021) Natural and conjugate mates of Frenet curves in three-dimensional Lie group. Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 70:1, pages 522-540.
Crossref
Jinhua Qian, Pei Yin, Xueshan Fu & Hongzeng Wang. (2021) Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space. Mathematics 9:12, pages 1451.
Crossref
Absos Ali Shaikh, Mohamd Saleem Lone & Pinaki Ranjan Ghosh. (2021) Rectifying curves under conformal transformation. Journal of Geometry and Physics 163, pages 104117.
Crossref
Kahraman Esen ÖZEN & Murat TOSUN. (2021) A New Moving Frame for Trajectories with Non-Vanishing Angular Momentum. Journal of Mathematical Sciences and Modelling 4:1, pages 7-18.
Crossref
Beyhan YILMAZ, İsmail GÖK & Yusuf YAYLI. (2021) Polynomial Parametric Equations of Rectifying Salkowski Curves. Gazi University Journal of Science 34:1, pages 211-219.
Crossref
Mehmet Önder. (2019) Construction of Curve Pairs and Their Applications. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 91:1, pages 21-28.
Crossref
Buddhadev PAL & Akhılesh YADAV. (2021) Some characterizations of rectifying curves in the 3-dimensional hyperbolic space $\mathbb H^{3}(-r)$. Hacettepe Journal of Mathematics and Statistics 50:1, pages 235-242.
Crossref
Mustafa Dede. (2020) Helical Extension Curve of a Space Curve. Mediterranean Journal of Mathematics 18:1.
Crossref
Rashad Abdel-Baky & Mohamed Khalifa Saad. (2021) Some characterizations of dual curves in dual 3-space $ \mathbb{D}^{3} $. AIMS Mathematics 6:4, pages 3339-3351.
Crossref
Vitor Balestro, Horst Martini & Makoto Sakaki. (2020) Differential geometry of spatial curves for gauges. São Paulo Journal of Mathematical Sciences 14:2, pages 496-509.
Crossref
Absos Ali Shaikh, Mohamd Saleem Lone & Pinaki Ranjan Ghosh. (2021) Normal Curves on a Smooth Immersed Surface. Indian Journal of Pure and Applied Mathematics 51:4, pages 1343-1355.
Crossref
Absos Ali Shaikh & Pinaki Ranjan Ghosh. (2020) Curves on a Smooth Surface with Position Vectors Lie in the Tangent Plane. Indian Journal of Pure and Applied Mathematics 51:3, pages 1097-1104.
Crossref
Mahmut MAK. (2020) Some characterizations of timelike rectifying curves in de sitter 3 space. Cumhuriyet Science Journal 41:2, pages 327-343.
Crossref
Zafar IQBAL & Joydeep SENGUPTA. (2020) Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$. Fundamental Journal of Mathematics and Applications 3:1, pages 8-16.
Crossref
Sezgin BÜYÜKKÜTÜK, İlim KİŞİ, Günay ÖZTÜRK & Kadri ARSLAN. (2020) Some Characterizations of Curves in n-dimensional Euclidean SpaceSome Characterizations of Curves in n-dimensional Euclidean Space. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi 10:2, pages 1273-1285.
Crossref
Absos Ali Shaikh, Mohamd Saleem Lone & Pinaki Ranjan Ghosh. (2020) Conformal image of an osculating curve on a smooth immersed surface. Journal of Geometry and Physics 151, pages 103625.
Crossref
Absos Ali Shaikh & Pinaki Ranjan Ghosh. (2020) Rectifying and Osculating Curves on a Smooth Surface. Indian Journal of Pure and Applied Mathematics 51:1, pages 67-75.
Crossref
Roa Makki. (2020) Some characterizations of non-null rectifying curves in dual Lorentzian 3-space $\mathbb{D}_{1}^{3}$. AIMS Mathematics 6:3, pages 2114-2131.
Crossref
Özgür Boyacıoğlu Kalkan. (2020) On normal curves and their characterizations in Lorentzian n-space. AIMS Mathematics 5:4, pages 3510-3524.
Crossref
Basak Ozulku Engin & Ahmet Yucesan. (2020) The characterizations of some special Frenet curves in Minkowski 3-space. Malaya Journal of Matematik 8:4, pages 2137-2143.
Crossref
Absos Ali Shaikh & Pinaki Ranjan Ghosh. (2019) Rectifying curves on a smooth surface immersed in the Euclidean space. Indian Journal of Pure and Applied Mathematics 50:4, pages 883-890.
Crossref
Bülent ALTUNKAYA. (2019) Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space. International Electronic Journal of Geometry 12:2, pages 229-240.
Crossref
Huili Liu, Yixuan Liu & Seoung Dal Jung. (2019) Associated spherical partner of space curve in Euclidean 3-space. Topology and its Applications 264, pages 79-88.
Crossref
Yongqiao Wang, Donghe Pei & Ruimei Gao. (2019) Generic Properties of Framed Rectifying Curves. Mathematics 7:1, pages 37.
Crossref
Tanju Kahraman. (2018) Some Null Quaternionic Curves in Minkowski spaces. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 14:4, pages 357-361.
Crossref
Özcan Bektaş. (2018) Normal curves in n-dimensional Euclidean space. Advances in Difference Equations 2018:1.
Crossref
Vishesh S. Bhat & R. Haribaskar. (2018) A pair of kinematically related space curves. International Journal of Geometric Methods in Modern Physics 15:10, pages 1850180.
Crossref
Serkan Öztürk & Melek Erdoğdu. (2018) Öklid Uzayında Sabit Oranlı Bertrand Eğrileri. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22:3, pages 1276-1282.
Crossref
Luiz C. B. da Silva & José Deibsom da Silva. (2018) Characterization of Curves that Lie on a Geodesic Sphere or on a Totally Geodesic Hypersurface in a Hyperbolic Space or in a Sphere. Mediterranean Journal of Mathematics 15:2.
Crossref
Kazim İlarslan, Nihal Kiliç & Hatice Altin Erdem. (2017) Osculating curves in 4-dimensional semi-Euclidean space with index 2. Open Mathematics 15:1, pages 562-567.
Crossref
Funda KAYMAZ & Ferdağ Kahraman AKSOYAK. (2017) Some Special Curves and Mannheim Curves in Three Dimensional Euclidean Space. Mathematical Sciences and Applications E-Notes 5:1, pages 34-39.
Crossref
Mihriban Kulahci. (2017) Investigation of a curve using Frenet frame in the lightlike cone. Open Physics 15:1, pages 175-181.
Crossref
Peter T. Ho, Lucy H. Odom & Bogdan D. Suceavă. (2015) On Chasles' Property of the Helicoid in Tri-Twisted Real Ambient Space. Analele Universitatii "Ovidius" Constanta - Seria Matematica 23:2, pages 121-132.
Crossref
Pascual Lucas & José Antonio Ortega-Yagües. (2015) Rectifying curves in the three-dimensional sphere. Journal of Mathematical Analysis and Applications 421:2, pages 1855-1868.
Crossref
Kazim İLARSLAN & Emilija NEŠOVIĆ. (2014) SOME RELATIONS BETWEEN NORMAL AND RECTIFYING CURVES IN MINKOWSKI SPACE-TIME. International Electronic Journal of Geometry 7:1, pages 26-35.
Crossref
Jin Ho Choi & Young Ho Kim. (2012) Associated curves of a Frenet curve and their applications. Applied Mathematics and Computation 218:18, pages 9116-9124.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.