Relevant bibliographies by topics / Bertrand curve

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Bertrand curve'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Bertrand curve"

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Öztekin, Handan. "Special Bertrand Curves in 4D Galilean Space." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/318458.

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The generalization of Bertrand curves in Galilean 4-space is introduced and the characterization of the generalized Bertrand curves is obtained. Furthermore, it is proved that no special curve is a classical Bertrand curve in Galilean 4-space such that the notion of classical Bertrand curve is definite only in three-dimensional spaces.
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Zhang, Chunxiao, and Donghe Pei. "Generalized Bertrand Curves in Minkowski 3-Space." Mathematics 8, no. 12 (2020): 2199. http://dx.doi.org/10.3390/math8122199.

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We define a generalized lightlike Bertrand curve pair and a generalized non-lightlike Bertrand curve pair, discuss their properties and prove the necessary and sufficient condition of a curve which is a generalized lightlike or a generalized non-lightlike Bertrand curve. Moreover, we study the relationship between slant helices and generalized Bertrand curves.
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Erdem, Hatice Altın, and Kazım İlarslan. "Spacelike Bertrand curves in Minkowski 3-space revisited." Analele Universitatii "Ovidius" Constanta - Seria Matematica 31, no. 3 (2023): 87–109. https://doi.org/10.2478/auom-2023-0033.

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Abstract In the geometry of curves in 𝔼3, if the principal normal vector field of a given space curve ϕ with non-zero curvatures is the principal normal vector field of another space curve ϕ *, then the curve ϕ is called a Bertrand curve and ϕ * is called Bertrand partner of ϕ. These curves have been studied in di erent space over a long period of time and found wide application in di erent areas. Therefore, we have a great knowledge of geometric properties of these curves. In this paper, revested results for spacelike Bertrand curves with non-null normal vectors will be given with the previou
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Li, Yanlin, Osman Keçilioğlu, and Kazım İlarslan. "Generalized Bertrand Curve Pairs in Euclidean Four-Dimensional Space." Axioms 14, no. 4 (2025): 253. https://doi.org/10.3390/axioms14040253.

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In this study, the existence of Bertrand curves (in the classical sense, i.e., curves with a common principal normal vector field) in four-dimensional Euclidean space is demonstrated using a novel approach. The necessary conditions for a regular curve to be a Bertrand curve pair are obtained. Furthermore, the relationship between Bertrand curves and Combescure-related curves (pairs of curves with parallel Frenet vectors) is established, and several geometric properties are derived. Additionally, examples are constructed for both Bertrand curve pairs and Combescure-related curve pairs, and thei
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Tamta, Stuti, and Ram Shankar Gupta. "New Parametrization of Bertrand Partner D-curves in $\mathbb{E}^{3}$." Boletim da Sociedade Paranaense de Matemática 42 (April 19, 2024): 1–11. http://dx.doi.org/10.5269/bspm.63309.

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We define and study a new parametrization of a Bertrand partner D-curve \{$\alpha$,$\alpha^{*}$\} in Euclidean 3-space by not taking Darboux frame element $g^{*}$ of Bertrand partner D-curve $\alpha^{*}$ parallel to $\overrightarrow{\alpha \alpha^{*}}$. We obtain a necessary and sufficient condition for a curve to be such type of Bertrand D-curves. Also, we obtain a characterization of a new parametrization of asymptotic Bertrand D-curves and provide an example.
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Aksoyak, Ferdag Kahraman, Ismail Gok, and Kazim Ilarslan. "Generalized Null Bertrand Curves In Minkowski Space-Time." Annals of the Alexandru Ioan Cuza University - Mathematics 60, no. 2 (2014): 489–502. http://dx.doi.org/10.2478/aicu-2013-0031.

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Abstract Çöken and ÇIFTCI proved that a null Cartan curve in Minkowski space-time E41 is a null Bertrand curve if and only if k2 is nonzero constant and k3 is zero. That is, the null curve with non-zero curvature k2 is not a Bertrand curve in Minkowski space-time E41. So, in this paper we defined a new type of Bertrand curve in Minkowski space-time E41 for a null curve with non-zero curvature k3 by using the similar idea of generalized Bertrand curve given by Matsuda and Yorozu and we called it a null (1, 3)-Bertrand curve. Also, we proved that if a null curve with non-zero curvatures in Minko
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ÖNDER, Mehmet. "Direction curves of generalized Bertrand curves and involute-evolute curves in $E^{4}$." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 2 (2022): 326–38. http://dx.doi.org/10.31801/cfsuasmas.950707.

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In this study, we define (1,3)-Bertrand-direction curve and (1,3)-Bertrand-donor curve in the 4-dimensional Euclidean space $E^{4}$. We introduce necessary and sufficient conditions for a special Frenet curve to have a (1,3)-Bertrand-direction curve. We introduce the relations between Frenet vectors and curvatures of these direction curves. Furthermore, we investigate whether (1,3)-evolute-donor curves in $E^{4}$ exist and show that there is no (1,3)-evolute-donor curve in $E^{4}$ .
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Kızıltuğ, Sezai, Mehmet Onder, and Omer Tarakçi. "Bertrand and Mannheim partner -curves on parallel surfaces." Boletim da Sociedade Paranaense de Matemática 35, no. 2 (2017): 159–69. http://dx.doi.org/10.5269/bspm.v35i2.24309.

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In this paper we study Bertrand and Mannheim partner -curves on parallel surface. Using the definition of parallel surfaces, first we find images of two curves lying on two different surfaces and satisfying the conditions to be Bertrand partner -curve or Mannheim partner -curve. Then we obtain relationships between Bertrand and Mannheim partner -curves and their image curves.
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Erdem, H. A., A. Uçum, K. İlarslan, and Ç. Camcı. "New approach to timelike Bertrand curves in 3-dimensional Minkowski space." Carpathian Mathematical Publications 15, no. 2 (2023): 482–94. http://dx.doi.org/10.15330/cmp.15.2.482-494.

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In the theory of curves in Euclidean $3$-space, it is well known that a curve $\beta $ is said to be a Bertrand curve if for another curve $\beta^{\star}$ there exists a one-to-one correspondence between $\beta $ and $\beta^{\star}$ such that both curves have common principal normal line. These curves have been studied in different spaces over a long period of time and found wide application in different areas. In this article, the conditions for a timelike curve to be Bertrand curve are obtained by using a new approach in contrast to the well-known classical approach for Bertrand curves in Mi
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DOĞAN YAZICI, Bahar, Osman Zeki OKUYUCU, and Murat TOSUN. "On special singular curve couples of framed curves in 3D Lie groups." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 72, no. 3 (2023): 710–20. http://dx.doi.org/10.31801/cfsuasmas.1197154.

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In this paper, we introduce Bertrand and Mannheim curves of framed curves, which are a special singular curve in 3D Lie groups. We explain the conditions for framed curves to be Bertrand curves and Mannheim curves in 3D Lie groups. We give relationships between framed curvatures and Lie curvatures of Bertrand and Mannheim curves of framed curves. In addition, we obtain the characterization of Bertrand and Mannheim curves according to the various frames of framed curves in 3D Lie groups.
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Dissertations / Theses on the topic "Bertrand curve"

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Flôres, Marcia Viaro. "HÉLICES, CURVAS DE BERTRAND E SUPERFÍCIES REGRADAS." Universidade Federal de Santa Maria, 2012. http://repositorio.ufsm.br/handle/1/9973.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>This work is designed to study helices and Bertrand curves. A circular helix is characterized by having constant curvature k 6= 0 and constant torsion t . If the ratio t k is constant, the curve is called generalized helix. A curve g : I −→R3 is called a Bertrand curve if there is another curve g : I −→R3 such that the normal lines of g and g at s ∈ I are equal. Generalized helices and Bertrand curves can be viewed as generalizations of the circular helix. In this work, we obtain important characterizations of these curves. Besides
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Bertrand, Fleurianne [Verfasser]. "Approximated flux boundary conditions for Raviart-Thomas finite elements on domains with curved boundaries and applications to first-order system least squares / Fleurianne Bertrand." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2014. http://d-nb.info/1063982103/34.

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Cheng, Yung-Ming, and 鄭永明. "On the Generalization of Bertrand Curves in a Euclidean n-space." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/09641166328261936890.

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碩士<br>國立臺灣師範大學<br>數學系<br>95<br>In an n-dimentional Euclidean space R^n, we prove that if a C^{infinity}-special Frenet curve C is a (i_1,...,i_m)-Bertrand curve then its Frenet (i_1,...,i_m)-normal plane at c(s) must contain the Frenet 1-normal line. In addition, we prove that if a (1,3)-Bertrand curve in R^4 has more than one (1,3)-Bertrand mate, then it has infinitely many Bertrand mates. This case occurs if and only if its curvature function k1 and the ratio of its curvature functions k2 and k3 are constant.
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Book chapters on the topic "Bertrand curve"

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Incesu, Muhsin, Sara Yilmaz Evren, and Osman Gursoy. "On the Bertrand Pairs of Open Non-Uniform Rational B-Spline Curves." In Springer Proceedings in Mathematics & Statistics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-8177-6_11.

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Russell, Bertrand, Richard A. Rempel, Bernd Frohmann, Mark Lippincott, and Margaret Moran. "War: The Cause and the Cure. Rulers Cannot Be Trusted with Peace Negotiations." In The Collected Papers of Bertrand Russell, Volume 13. Routledge, 2024. http://dx.doi.org/10.4324/9781003556596-5.

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WU, WENJUN (WU WEN-TSUN). "A MECHANIZATION METHOD OF GEOMETRY AND ITS APPLICATIONS: II. CURVE PAIRS OF BERTRAND TYPE." In Selected Works of Wen-Tsun Wu. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812791085_0020.

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"Directional Bertrand Curves in Minkowski Space." In INNOVATIVE RESEARCH IN NATURAL SCIENCE AND MATHEMATICS. DUVAR PUBLISHING, 2023. http://dx.doi.org/10.59287/irnsm.607.

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Grosholz, Emily R. "Leibniz on Transcendental Curves." In Representation and Productive Ambiguity in Mathematics and the Sciences. Oxford University PressOxford, 2007. http://dx.doi.org/10.1093/oso/9780199299737.003.0008.

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Abstract When Louis Couturat and Bertrand Russell enlisted Leibniz as the champion of logicism, in the search for a single perfect idiom for the truths of mathematics and science, they dismissed at the same time much of his writing on theology and metaphysics. This was of course a brutal triage that generations of scholars throughout the twentieth century have critically examined and rejected, but in the Anglophone world we have only recently begun to assess properly how it distorts our understanding of Leibniz’s account of mathematics and science.
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"Can Religion Cure Our Troubles? [1955]." In The Collected Papers of Bertrand Russell (Volume 28). Routledge, 2003. http://dx.doi.org/10.4324/9780203009185-37.

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Graf, William L. "Plutonium and Los Alamos." In Plutonium and the Rio Grande. Oxford University Press, 1995. http://dx.doi.org/10.1093/oso/9780195089332.003.0007.

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The plutonium in the Northern Rio Grande is entirely artificial. Small amounts of plutonium may have formed in exceptionally rich uranium deposits in south-central Africa, but for practical purposes, until its manufacture in 1939, the element did not occur in the earth’s environment. Although the detailed story of the origins of plutonium are beyond the scope of this book, a summary of that history does clarify the issues regarding plutonium in the Northern Rio Grande in the late twentieth century. The purposes of this chapter are to review the origins of plutonium and to examine briefly the n
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Conference papers on the topic "Bertrand curve"

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Şenyurt, Süleyman, Yasin Altun, and Ceyda Cevahir. "Smarandache curves according to Sabban frame of fixed pole curve belonging to the Bertrand curves pair." In INTERNATIONAL CONFERENCE ON ADVANCES IN NATURAL AND APPLIED SCIENCES: ICANAS 2016. Author(s), 2016. http://dx.doi.org/10.1063/1.4945871.

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