Relevant bibliographies by topics / Biharmonic curve

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

Academic literature on the topic 'Biharmonic curve'

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

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Journal articles on the topic "Biharmonic curve"

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Gningue, Mamadou, Ameth Ndiaye, and Rénovat Nkunzimana. "Biharmonic Curves in a Strict Walker 3-Manifold." International Journal of Mathematics and Mathematical Sciences 2022 (February 22, 2022): 1–6. http://dx.doi.org/10.1155/2022/3855033.

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In this paper, we study the geometry of biharmonic curves in a strict Walker 3-manifold and we obtain explicit parametric equations for biharmonic curves and time-like biharmonic curves, respectively. We discuss the conditions for a speed curve to be a slant helix in a Walker manifold. We give an example of biharmonic curve for illustrating the main result.
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Karakaş, Gizem Köprülü, and Bayram Şahin. "Biharmonic curves along Riemannian submersions." Miskolc Mathematical Notes 25, no. 2 (2024): 805. https://doi.org/10.18514/mmn.2024.4375.

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The purpose of this paper is to study biharmonic curves along Riemannian submersions. We first consider a Riemannian submersion from a Riemannian manifold onto Riemannian manifold and investigate under what conditions a biharmonic curve on the total manifold is transformed to a biharmonic curve on the base manifold. We obtain several results with certain restrictions on curvatures. We then consider a Riemannian submersion from a Kaehler manifold onto a Riemannian manifold. Necessary and sufficient conditions were obtained for a curve that is biharmonic in the total manifold of Riemannian subme
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Körpınar, Talat, and Essin Turhan. "Biharmonic curves according to parallel transport frame in E⁴." Boletim da Sociedade Paranaense de Matemática 31, no. 2 (2013): 213. http://dx.doi.org/10.5269/bspm.v31i2.17669.

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Turhan, Essin, and Talat Körpinar. "On Characterization Canal Surfaces around Timelike Horizontal Biharmonic Curves in Lorentzian Heisenberg Group Heis3." Zeitschrift für Naturforschung A 66, no. 6-7 (2011): 441–49. http://dx.doi.org/10.1515/zna-2011-6-709.

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In this paper, we describe a new method for constructing a canal surface surrounding a timelike horizontal biharmonic curve in the Lorentzian Heisenberg group Heis3. Firstly, we characterize timelike biharmonic curves in terms of their curvature and torsion. Also, by using timelike horizontal biharmonic curves, we give explicit parametrizations of canal surfaces in the Lorentzian Heisenberg group Heis3
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Körpinar, Talat, and Essin Turhan. "Tubular Surfaces Around Timelike Biharmonic Curves in Lorentzian Heisenberg Group Heis3." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 1 (2012): 431–46. http://dx.doi.org/10.2478/v10309-012-0029-0.

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Abstract In this paper, we describe a new method for constructing a tubular surface surrounding a timelike biharmonic curve in the Lorentzian Heisenberg group Heis3. Firstly, we characterize timelike biharmonic curves in terms of their curvature and torsion. Also, by using timelike biharmonic curves, we give explicit parametrizations of tubular surfaces in the Lorentzian Heisenberg group Heis3.
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Körp?nar, T., and E. Turhan. "Inextensible Flows of Tangent Developable Surfaces of Biharmonic Curves in SL2?(R)." Journal of Scientific Research 4, no. 2 (2012): 365. http://dx.doi.org/10.3329/jsr.v4i2.8987.

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We present some results on the inextensible flows of tangent developable surfaces of biharmonic curves in the . Finally, we find out explicit parametric equations tangent developable surfaces of biharmonic curves in the . Keywords: Biharmonic curve;Inextensible flows. © 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v4i2.8987 J. Sci. Res. 4 (2), 365-371 (2012)
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Ceylan, Ayse, and Abdullah Ergin. "Mannheim partner curves in Cartan-Vranceanu 3-space." Filomat 30, no. 4 (2016): 1089–95. http://dx.doi.org/10.2298/fil1604089y.

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In this paper, the Mannheim mate curves of the proper biharmonic curves in Cartan-Vranceanu 3-dimensional spaces (M,ds2l,m), with l2 ? 4m and m ? 0 are studied. We give the definition of the Mannheim mate of a proper biharmonic curve and give the explicit parametric equations of that Mannheim mate curve in Cartan-Vranceanu 3-dimensional space. Moreover, we show that the distance between corresponding points of the Mannheim pairs is constant in Cartan-Vranceanu 3-dimensional spaces.
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Cakir, Osman, and Suleyman Senyurt. "Harmonicity and differential equation of involute of a curve in E3." Thermal Science 23, Suppl. 6 (2019): 2119–25. http://dx.doi.org/10.2298/tsci190730401c.

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In this paper, we first give necessary conditions in which we can decide whether a given curve is biharmonic or 1-type harmonic and differential equations characterizing the regular curves. Then we research the Frenet formulas of involute of a unit speed curve by making use of the relations between the involute of a curve and the curve itself. In addition we apply these formulas to define the essential conditions by which one can determine whether the involute of a unit speed curve is biharmonic or 1-type harmonic and then we write differential equations characterizing the involute curve by me
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Tang, Wanxiao, Pradip Majhi, Peibiao Zhao, and Uday De. "Legendre curves on 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection." Filomat 32, no. 10 (2018): 3651–56. http://dx.doi.org/10.2298/fil1810651t.

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The object of the present paper is to study biharmonic Legendre curves, locally ?-symmetric Legendre curves and slant curves in 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection. Finally, we construct an example of a Legendre curve in a 3-dimensional Kenmotsu manifold.
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Karakaş, Köprülü, and Bayram Şahin. "Biharmonic curves along Riemannian maps." Filomat 38, no. 1 (2024): 227–39. http://dx.doi.org/10.2298/fil2401227k.

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In this paper, the transformation of a bi-harmonic curve on the total manifold into a bi-harmonic curve on the base manifold along a Riemannian map between Riemannian manifolds is examined. In this direction, first, necessary and sufficient conditions are obtained for the Riemannian map between two Riemannian manifolds for the curve on the total manifold to be bi-harmonic curve on the base manifold. Afterwards, the case that the total manifold is a complex space form was taken into consideration and the bi-harmonic character of the curve on the base manifold was examined by considering appropr
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Dissertations / Theses on the topic "Biharmonic curve"

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Larsson, Karl. "Finite Element Methods for Thin Structures with Applications in Solid Mechanics." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-79297.

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Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers. In the first paper we introduce a thread model for use i
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Book chapters on the topic "Biharmonic curve"

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"Biharmonic Curves and Surfaces in Pseudo-Euclidean Spaces." In Biharmonic Submanifolds and Biharmonic Maps in Riemannian Geometry. WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811212383_0004.

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Conference papers on the topic "Biharmonic curve"

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Acet, Bilal Eftal, Selcen Yüksel Perktaş, and Feyza Esra Erdoğan. "A study on f-biharmonic curves in S(1,4)." In 1ST INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES (ICMRS 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5047874.

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Perktaş, Selcen Yüksel, Adara M. Blaga, Bilal Eftal Acet, and Feyza Esra Erdoğan. "Magnetic biharmonic curves on 3-dimensional normal almost paracontact metric manifolds." In 1ST INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES (ICMRS 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5047877.

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Perktaş, Selcen Yüksel, and Feyza Esra Erdoğan. "Biharmonic slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds." In II. INTERNATIONAL CONFERENCE ON ADVANCES IN NATURAL AND APPLIED SCIENCES: ICANAS 2017. Author(s), 2017. http://dx.doi.org/10.1063/1.4981674.

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Perktaş, Selcen Yüksel, and Bilal Eftal Acet. "Biharmonic Frenet and non-Frenet Legendre curves in 3-dimensional normal almost paracontact metric manifolds." In II. INTERNATIONAL CONFERENCE ON ADVANCES IN NATURAL AND APPLIED SCIENCES: ICANAS 2017. Author(s), 2017. http://dx.doi.org/10.1063/1.4981673.

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Journal articles
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