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Relevant bibliographies by topics / TN-Smarandache curves

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Journal articles

Academic literature on the topic 'TN-Smarandache curves'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "TN-Smarandache curves"

1

KUCUKARSLAN YUZBASİ, Zuhal, and Sevinç TAZE. "On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group." Journal of New Theory, no. 40 (September 30, 2022): 82–89. http://dx.doi.org/10.53570/jnt.1165809.

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This paper finds sufficient conditions to determine a surface whose mean curvature along a given Smarandache curve is constant in a three-dimensional Lie group. This is accomplished by using the Frenet frames of the specified curve to express surfaces that span the TN, NB, and TB Smarandache curves parametrically. In terms of the curvatures of given Smarandache curves, marching scale functions, and their partial derivatives, the mean curvatures of these surfaces along the given TN, NB, and TB Smarandache curves are determined. Sufficient conditions are found to maintain the provided mean curva

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2

İsabeyoǧlu, Zeynep, Tülay Erişir, and Ayşe Zeynep Azak. "Spinor Equations of Smarandache Curves in E3." Mathematics 12, no. 24 (2024): 4022. https://doi.org/10.3390/math12244022.

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This study examines the spinor representations of TN (tangent and normal), NB (normal and binormal), TB (tangent and binormal) and TNB (tangent, normal and binormal)–Smarandache curves in three-dimensional Euclidean space E3. Spinors are complex column vectors and move on Pauli spin matrices. Isotropic vectors in the C3 complex vector space form a two-dimensional surface in the C2 complex space. Additionally, each isotropic vector in C3 space corresponds to two vectors in C2 space, called spinors. Based on this information, our goal is to establish a relationship between curve theory in differ

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3

K�rpinar, Talat, and Essin TURHAN. "Smarandache TN Curves Of General Helices In The Sol3 Space." i-manager’s Journal on Mathematics 1, no. 3 (2012): 1–5. http://dx.doi.org/10.26634/jmat.1.3.1938.

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4

Ouarab, Soukaina. "Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in E 3." Abstract and Applied Analysis 2021 (March 31, 2021): 1–8. http://dx.doi.org/10.1155/2021/5526536.

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In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E 3 . It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.

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5

Ouarab, Soukaina. "Corrigendum to “Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in E 3 ”." Abstract and Applied Analysis 2022 (July 11, 2022): 1–7. http://dx.doi.org/10.1155/2022/9849574.

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In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E 3 . It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.

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6

GURSES, NURTEN (BAYRAK), OZCAN BEKTAS, and SALIM YUCE. "SPECIAL SMARANDACHE CURVES IN R3." January 19, 2016. https://doi.org/10.5281/zenodo.234127.

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In this study, we determine TN-Smarandache curves whose position vector is composed by Frenet frame vectors of another regular curve in Minkowski 3-space R3 1. Then, we present some characterisations of Smarandache curves and calculate Frenet invariants of these curves.

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7

NURTEN, (BAYRAK) GÜRSES, BEKTAS ÖZCAN, and YÜCE SALIM. "SPECIAL SMARANDACHE CURVES IN R." June 13, 2016. https://doi.org/10.5281/zenodo.835466.

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In this study, we determine TN-Smarandache curves whose position vector is composed by Frenet frame vectors of another regular curve in Minkowski 3-space R<sup>3</sup><sub>1</sub>. Then, we present some characterisations of Smarandache curves and calculate Frenet invariants of these curves.

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8

Tamta, Stuti, and Ram Shankar Gupta. "POINTWISE 1-TYPE GAUSS MAP OF DEVELOPABLE SMARANDACHE RULED SURFACES IN $\mathbb{E}^{3}$." Facta Universitatis, Series: Mathematics and Informatics, December 20, 2023, 741. http://dx.doi.org/10.22190/fumi230504048t.

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In this paper, we study developable TN, TB, and NB-Smarandache ruled surface with pointwise 1-type Gauss map. In particular, we obtain every such developable TN-Smarandache ruled surface has constant mean curvature, developable TB Smarandache ruled surface is minimal if and only if the curve is a planar curve or helix, and developable NB-Smarandache ruled surface is always plane. Also, we give some examples.

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