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Journal articles on the topic 'Biharmonic curve'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

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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2

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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3

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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4

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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5

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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7

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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8

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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9

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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10

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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11

Ilbery, Peter, Luke Kendall, Cyril Concolato, and Michael McCosker. "Biharmonic diffusion curve images from boundary elements." ACM Transactions on Graphics 32, no. 6 (2013): 1–12. http://dx.doi.org/10.1145/2508363.2508426.

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12

CAN, Saniye, and Çetin CAMCI. "Generalized Cross Product in (2+s)-Dimensional Framed Metric Manifolds with Application to Legendre Curves." Journal of New Theory, no. 42 (March 31, 2023): 94–107. http://dx.doi.org/10.53570/jnt.1213002.

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This study generalizes the cross product defined in 3-dimensional almost contact metric manifolds and describes a new generalized cross product for n=1 in (2n+s)-dimensional framed metric manifolds. Moreover, it studies some of the proposed product’s basic properties. It also performs characterizations of the curvature of a Legendre curve on an S-manifold and calculates the curvature of a Legendre curve. Furthermore, it shows that Legendre curves are also biharmonic curves. Next, this study observes that a Legendre curve of osculating order 5 on S-manifolds is imbedded in the 3-dimensional K-c

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13

Khalil, Abdelouahed El, Siham Kellati, and Abdelfattah Touzani. "On the principal frequency curve of the p-biharmonic operator." Arab Journal of Mathematical Sciences 17, no. 2 (2011): 89–99. http://dx.doi.org/10.1016/j.ajmsc.2011.01.002.

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14

Laghzal, Mohamed, Abdelouahed El Khalil, My Driss Morchid Alaoui, and Abdelfattah Touzani. "Eigencurves of the p(·)-Biharmonic operator with a Hardy-type term." Moroccan Journal of Pure and Applied Analysis 6, no. 2 (2020): 198–209. http://dx.doi.org/10.2478/mjpaa-2020-0015.

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AbstractThis paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the p(·)-biharmonic operator and a Hardy-type term that depend on the solution and with a parameter λ. By using a variational approach and min-max argument based on Ljusternik-Schnirelmann theory on C1-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve μ1(λ) and also show that, the smallest curve μ1(λ) is positive for all 0 ≤ λ < CH, with CH is the o

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15

CEYLAN, Ayşe Yilmaz, and Abdullah Aziz ERGİN. "BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE." International Electronic Journal of Geometry 8, no. 1 (2015): 45–52. http://dx.doi.org/10.36890/iejg.592796.

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16

LESNIC, D., and A. ZEB. "THE METHOD OF FUNDAMENTAL SOLUTIONS FOR AN INVERSE INTERNAL BOUNDARY VALUE PROBLEM FOR THE BIHARMONIC EQUATION." International Journal of Computational Methods 06, no. 04 (2009): 557–67. http://dx.doi.org/10.1142/s0219876209001991.

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In this paper, an inverse internal boundary value problem associated to the biharmonic equation is considered. The problem consists of determining unknown boundary conditions from extra interior measurements. The method of fundamental solutions (MFS) is used to discretize the problem and the resulting ill-conditioned system of linear equations is solved using the Tikhonov regularization technique. It is shown that, unlike the least-squares method, the MFS-regularization numerical technique produces stable and accurate numerical solutions for an appropriate choice of the regularization paramete

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17

Lei, Sun. "A New General Solution of Axisymmetric Elastic Space Problem in Pavement Engineering." Mathematical Problems in Engineering 2023 (February 22, 2023): 1–10. http://dx.doi.org/10.1155/2023/5308832.

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The general solution of the axial symmetry elastic space problem in cement concrete pavement is an elementary question. Combining the Love method and the Southwell method, the Southwell operator was used in the variable selection process, the displacement function was introduced to express the displacement component by the Love method, the expression of stress indicated by the displacement function was obtained by combining the displacement components, geometric equations, and physical equations, then the stress was substituted into the equilibrium equation, the biharmonic equation of displace

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18

Genda, Attila, Alexander Fidlin, and Oleg Gendelman. "On the escape of a resonantly excited couple of particles from a potential well." Nonlinear Dynamics 104, no. 1 (2021): 91–102. http://dx.doi.org/10.1007/s11071-021-06312-7.

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AbstractThe escape dynamics of a damped system of two coupled particles in a truncated potential well under biharmonic excitation are investigated. It is assumed that excitation frequencies are tuned to the modal natural frequency of the relative motion and to the modal frequency of the centre of mass on the bottom of the potential well. Although the escape is essentially a non-stationary process, the critical force strongly depends on the stationary amplitude of the relative vibrations within the pair of masses. The characteristic escape curve for the critical force moves up on the frequency-

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19

Turhan, Essin, and Talat Körpinar. "On Characterization of Time-Like Horizontal Biharmonic Curves in the Lorentzian Heisenberg Group Heis3." Zeitschrift für Naturforschung A 65, no. 8-9 (2010): 641–48. http://dx.doi.org/10.1515/zna-2010-8-904.

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In this paper, we study energy of time-like horizontal biharmonic curves in the Lorentzian Heisenberg group Heis3. We characterize the biharmonic curves in terms of their curvature and torsion. We prove that all of the biharmonic curves are helices. Finally, we study the mechanics of biharmonic curves and provide conditions for energy of horizontal biharmonic curves

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20

AYDIN, Tuba AĞIRMAN, and Hüseyin KOCAYİĞİT. "1-TYPE AND HARMONIC 1-TYPE TIMELIKE CURVES IN SEMI-EUCLIDEAN SPACE 42." Euroasia Journal of Mathematics, Engineering, Natural & Medical Sciences 8, no. 17 (2021): 217–23. http://dx.doi.org/10.38065/euroasiaorg.709.

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In the present study we consider 1-type, biharmonic, weak biharmonic and harmonic 1-type curves in semi-Euclidean space 42R according to the timelike Frenet frame. We give some characterizations and classifications of these type curves.

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21

Bozdağ, Şerife Nur. "A study on magnetic curves in trans-Sasakian manifolds." Analele Universitatii "Ovidius" Constanta - Seria Matematica 31, no. 3 (2023): 47–60. https://doi.org/10.2478/auom-2023-0031.

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Abstract In this paper, we focused on biharmonic, f-harmonic and f-biharmonic magnetic curves in trans-Sasakian manifolds. Moreover, we obtain necessary and su cient conditions for magnetic curves as well as Legendre magnetic curves to be biharmonic, f-harmonic and f-biharmonic. We investigate the states of these conditions in α-Sasakian, β-Kenmotsu and cosymplectic manifolds. Besides, we obtain some nonexistence theorems.

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22

MONTALDO, S., and A. RATTO. "BIHARMONIC CURVES INTO QUADRICS." Glasgow Mathematical Journal 57, no. 1 (2014): 131–41. http://dx.doi.org/10.1017/s0017089514000172.

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AbstractWe develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves in surfaces defined by a polynomial equation: In particular, we use it to give a complete classification of biharmonic curves in real quadrics of the three-dimensional Euclidean space.

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23

Körpınar, Talat, and Essin Turhan. "Biharmonic S-curves according to Sabban frame in Heisenberg group Heis³." Boletim da Sociedade Paranaense de Matemática 31, no. 1 (2012): 205. http://dx.doi.org/10.5269/bspm.v31i1.15761.

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In this paper, we study biharmonic curves accordig to Sabban frame in the Heisenberg group Heis³. We characterize the biharmonic curves in terms of their geodesic curvature and we prove that all of biharmonic curves are helices in the Heisenberg group Heis³. Finally, we find out their explicit parametric equations according to Sabban Frame.

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24

Belarbi, Mansour, Hichem Elhendi, and Lakehal Belarbi. "Biharmonic Curves in Three-Dimensional Generalized Symmetric Spaces." Journal of the Indian Mathematical Society 89, no. 3-4 (2022): 263. http://dx.doi.org/10.18311/jims/2022/29627.

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In this paper, we study biharmonic curves in three-dimensio -nal generalized symmetric spaces, equipped with a left-invariant pseudo- Riemannian metric. We characterize non-geodesic biharmonic curves in three-dimensional generalized symmetric spaces and prove that there ex- ists no non-geodesic biharmonic spacelike helix in three-dimensional gen- eralized symmetric spaces. We also show that a linear map from a Eu- clidean space in three-dimensional generalized symmetric spaces is bihar- monic if and only if it is a harmonic map, and give a complete classification of such maps.

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25

Körpınar, Talat, and Essin Turhan. "CHARACTERIZATION OF SPACELIKE BIHARMONIC CURVES WITH TIMELIKE BINORMAL ACCORDING TO FLAT METRIC IN LORENTZIAN HEISENBERG GROUP Heis³ - doi: 10.5269/bspm.v30i2.14706." Boletim da Sociedade Paranaense de Matemática 30, no. 2 (2011): 101–7. http://dx.doi.org/10.5269/bspm.v30i2.14706.

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In this paper, we study spacelike biharmonic curves with timelike binormal according to flat metric in the Lorentzian Heisenberg group Heis³. We characterize spacelike biharmonic curves with timelike binormal in terms of their curvature and torsion. Additionally, we determine the parametric representation of the spacelike biharmonic curves with timelike binormal according to flat metric from this characterization.

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26

Wang, Ze-Ping, and Li-Hua Qin. "f-Biharmonic Submanifolds in Space Forms and f-Biharmonic Riemannian Submersions from 3-Manifolds." Mathematics 12, no. 8 (2024): 1184. http://dx.doi.org/10.3390/math12081184.

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f-biharmonic maps are generalizations of harmonic maps and biharmonic maps. In this paper, we give some descriptions of f-biharmonic curves in a space form. We also obtain a complete classification of proper f-biharmonic isometric immersions of a developable surface in R3 by proving that a proper f-biharmonic developable surface exists only in the case where the surface is a cylinder. Based on this, we show that a proper biharmonic conformal immersion of a developable surface into R3 exists only in the case when the surface is a cylinder. Riemannian submersions can be viewed as a dual notion o

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27

KARACA, Fatma, and Cihan ÖZGÜR. "On f-Biharmonic Curves." International Electronic Journal of Geometry 11, no. 2 (2018): 18–27. http://dx.doi.org/10.36890/iejg.545115.

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28

Körpinar, Talat, and Essin Turhan. "On characterization of horizontal biharmonic curves in H^2 × R." Acta et Commentationes Universitatis Tartuensis de Mathematica 15, no. 2 (2020): 35–41. http://dx.doi.org/10.12697/acutm.2011.15.08.

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In this paper, we study biharmonic curves in H2 × R. We show that all of them are helices. By using the curvature and torsion of the curves, we give some characterizations of horizontal biharmonic curves in H2 × R.

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29

Montaldo, S., and A. Pámpano. "Totally biharmonic hypersurfaces in space forms and 3-dimensional BCV spaces." International Journal of Mathematics 32, no. 04 (2021): 2150025. http://dx.doi.org/10.1142/s0129167x21500257.

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A hypersurface is said to be totally biharmonic if all its geodesics are biharmonic curves in the ambient space. We prove that a totally biharmonic hypersurface into a space form is an isoparametric biharmonic hypersurface, which allows us to give the full classification of totally biharmonic hypersurfaces in these spaces. Moreover, restricting ourselves to the 3-dimensional case, we show that totally biharmonic surfaces into Bianchi–Cartan–Vranceanu spaces are isoparametric surfaces and we give their full classification. In particular, we show that, leaving aside surfaces in the 3-dimensional

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30

Inoguchi, Jun-Ichi. "Biharmonic curves in Minkowski3-space." International Journal of Mathematics and Mathematical Sciences 2003, no. 21 (2003): 1365–68. http://dx.doi.org/10.1155/s016117120320805x.

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31

Körpinar, Talat, та Essin Turhan. "Integral equations of biharmonic constant π₁-slope curves according to type-2 Bishop frame in the SOL space". Boletim da Sociedade Paranaense de Matemática 31, № 2 (2013): 205. http://dx.doi.org/10.5269/bspm.v31i2.17619.

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In this paper, we study biharmonic constant Π₁- slope curves according to type-2 Bishop frame in the SOL³. We characterize the biharmonic constant Π₁- slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric integral equations in the SOL³.

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32

Inoguchi, Jun-Ichi. "Biharmonic curves in Minkowski3-space. Part II." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–4. http://dx.doi.org/10.1155/ijmms/2006/92349.

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33

Voicu, Nicoleta. "BIHARMONIC CURVES IN FINSLER SPACES." Journal of the Korean Mathematical Society 51, no. 6 (2014): 1105–22. http://dx.doi.org/10.4134/jkms.2014.51.6.1105.

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34

Hüseyin ; HACISALIHOĞ LU, KOCAYIĞIT. "Biharmonic curves in contact geometry." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 61, no. 2 (2012): 35–43. http://dx.doi.org/10.1501/commua1_0000000678.

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35

Arslan, K., R. Ezentas, C. Murathan та T. Sasahara. "Biharmonic submanifolds in3-dimensional(κ,μ)-manifolds". International Journal of Mathematics and Mathematical Sciences 2005, № 22 (2005): 3575–86. http://dx.doi.org/10.1155/ijmms.2005.3575.

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Biharmonic maps between Riemannian manifolds are defined as critical points of the bienergy and generalized harmonic maps. In this paper, we give necessary and sufficient conditions for nonharmonic Legendre curves and anti-invariant surfaces of3-dimensional(κ,μ)-manifolds to be biharmonic.

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36

Perktaş, Selcen, Adara Blaga, Feyza Erdoğan, and Bilal Acet. "Bi-f-harmonic curves and hypersurfaces." Filomat 33, no. 16 (2019): 5167–80. http://dx.doi.org/10.2298/fil1916167p.

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In the present paper, we study bi-f-harmonic maps which generalize not only f-harmonic maps, but also biharmonic maps. We derive bi-f-harmonic equations for curves in the Euclidean space, unit sphere, hyperbolic space, and for hypersurfaces of Riemannian manifolds.

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37

Montaldo, Stefano, and Irene I. Onnis. "Biharmonic curves on an invariant surface." Journal of Geometry and Physics 59, no. 3 (2009): 391–99. http://dx.doi.org/10.1016/j.geomphys.2008.11.011.

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38

Güvenç, Şaban, and Ö. ÖzgurCihan. "On the characterizations of f-biharmonic legendre curves in Sasakian space forms." Filomat 31, no. 3 (2017): 639–48. http://dx.doi.org/10.2298/fil1703639g.

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39

Du, Li, and Juan Zhang. "Classification of f-Biharmonic Curves in Lorentz–Minkowski Space." Journal of Mathematics 2020 (August 18, 2020): 1–8. http://dx.doi.org/10.1155/2020/7529284.

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40

Abrunheiro, Lígia, and Margarida Camarinha. "An Intrinsic Version of the k-Harmonic Equation." Mathematics 11, no. 17 (2023): 3628. http://dx.doi.org/10.3390/math11173628.

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The notion of k-harmonic curves is associated with the kth-order variational problem defined by the k-energy functional. The present paper gives a geometric formulation of this higher-order variational problem on a Riemannian manifold M and describes a generalized Legendre transformation defined from the kth-order tangent bundle TkM to the cotangent bundle T*Tk−1M. The intrinsic version of the Euler–Lagrange equation and the corresponding Hamiltonian equation obtained via the Legendre transformation are achieved. Geodesic and cubic polynomial interpolation is covered by this study, being explo

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41

Inoguchi, Jun-ichi, and Ji-Eun Lee. "Biharmonic curves in f-Kenmotsu 3-manifolds." Journal of Mathematical Analysis and Applications 509, no. 1 (2022): 125941. http://dx.doi.org/10.1016/j.jmaa.2021.125941.

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42

K�rpinar, Talat, and Essin TURHAN. "Biharmonic Curves With Bishop Frame In E3." i-manager’s Journal on Mathematics 1, no. 4 (2012): 8–11. http://dx.doi.org/10.26634/jmat.1.4.2044.

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43

Fetcu, Dorel. "BIHARMONIC LEGENDRE CURVES IN SASAKIAN SPACE FORMS." Journal of the Korean Mathematical Society 45, no. 2 (2008): 393–404. http://dx.doi.org/10.4134/jkms.2008.45.2.393.

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44

Caddeo, Renzo, Stefano Montaldo, Cezar Oniciuc, and Paola Piu. "The Euler-Lagrange Method for Biharmonic Curves." Mediterranean Journal of Mathematics 3, no. 3-4 (2006): 449–65. http://dx.doi.org/10.1007/s00009-006-0090-x.

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45

KORPINAR, ZELIHA, та TALAT KORPINAR. "SMARANDACHE Π1B CURVES OF BIHARMONIC NEW TYPE CONSTANT Π2 - SLOPE CURVES ACCORDING TO TYPE-2 BISHOP FRAME IN THE SOL SPACE". Journal of Science and Arts 21, № 3 (2021): 681–88. http://dx.doi.org/10.46939/j.sci.arts-21.3-a08.

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In this paper, we study Smarandache Π1B curves of biharmonic new type constant Π2 -slope curves according to type-2 Bishop frame in the Sol space. Type-2 Bishop equations of Smarandache Π1B curves are obtained in terms of base curve's type-2 Bishop invariants. Subsequently, we express some interesting relations.

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46

Altunbas, Murat. "A Note on f-Biharmonic Curves in Lorentzian Heisenberg and Lorentzian Sol<sub>3</sub> Spaces." Journal of the Indian Mathematical Society 89, no. 3-4 (2022): 215. http://dx.doi.org/10.18311/jims/2022/28375.

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47

SASAHARA, TORU. "BIHARMONIC SUBMANIFOLDS IN NONFLAT LORENTZ 3-SPACE FORMS." Bulletin of the Australian Mathematical Society 85, no. 3 (2011): 422–32. http://dx.doi.org/10.1017/s0004972711002978.

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48

Körpinar, Talat, and Essin Turhan. "b-Smarandache tm₂ curves of biharmonic new type b-slant helices according to Bishop frame in the Sol space Sol³." Boletim da Sociedade Paranaense de Matemática 31, no. 2 (2013): 265. http://dx.doi.org/10.5269/bspm.v31i2.18273.

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In this paper, we study b-Smarandache tm₂ curves of biharmonic new type b-slant helix in the Sol³. We characterize the b-Smarandache tm₂ curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric equations in the Sol³.

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49

Cao, Xiangzhi, and Yong Luo. "On p-biharmonic submanifolds in nonpositively curved manifolds." Kodai Mathematical Journal 39, no. 3 (2016): 567–78. http://dx.doi.org/10.2996/kmj/1478073773.

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Luo, Yong. "On biharmonic submanifolds in non-positively curved manifolds." Journal of Geometry and Physics 88 (February 2015): 76–87. http://dx.doi.org/10.1016/j.geomphys.2014.11.004.

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