On the Framed Normal Curves in Euclidean 4-space

Yıldız, Önder Gökmen; Akyiğit, Mahmut

doi:10.33401/fujma.992917

Cited by 3 publications

(1 citation statement)

References 11 publications

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“…For instance, the Bertrand and Mannheim curve pairs of framed curves were considered by [21], and evolutes and focal surfaces of framed immersions were constructed in Euclidean 3-space in [22]. In addition, framed slant helices [23], generalized oscillating type ruled surfaces of singular curves in Euclidean 3-space [24], and framed normal curves in Euclidean 4-space [25] are recent studies using this frame.…”

Section: Introductionmentioning

confidence: 99%

Framed Curve Families Induced by Real and Complex Coupled Dispersionless-Type Equations

Popović¹,

Eren

Savić³

et al. 2023

Mathematics

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In this study, we investigate coupled real and complex dispersionless equations for curve families, even if they have singular points. Even though the connections with the differential equations and regular curves were considered in various ways in the past, since each curve does not need to be regular, we establish the connections for framed base curves, which generalize regular curves with linear independent conditions. Also, we give the Lax pairs of the real and complex coupled dispersionless equations from the motions of any framed curve. These give us significant conditions based on the framed curvatures and associated curvatures of the framed curves for integrability since it is well known that the Lax pair provides the integrability of differential equations.

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Section: Introductionmentioning

confidence: 99%

Framed Curve Families Induced by Real and Complex Coupled Dispersionless-Type Equations

Popović¹,

Eren

Savić³

et al. 2023

Mathematics

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A New Insight on Rectifying-Type Curves in Euclidean 4-Space

İşbilir,

Tosun

2023

International Electronic Journal of Geometry

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In this study, our purpose is to determine the generalized rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space $E_4$. Also, some characterizations of them are given. We construct some correlations between curvatures and invariants of generalized rectifying-type curves. Additionally, we obtain an illustrative example with respect to the rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space $E_4$.

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The developable surfaces with pointwise 1-type Gauss map of Frenet type framed base curves in Euclidean 3-space

Liu

Eren

Ayvacı

et al. 2022

MATH

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<abstract><p>In this study, the ruled developable surfaces with pointwise 1-type Gauss map of Frenet-type framed base (Ftfb) curve are introduced in Euclidean 3-space. The tangent developable surfaces, focal developable surfaces, and rectifying developable surfaces with singular points are considered. Then the conditions for the Gauss map of these surfaces to be pointwise 1-type are obtained separately. In order to form a basis for the study, first, the basic concepts related to the Ftfb curve and the Gauss map of a surface are recalled. Later, the necessary and sufficient conditions are found for these surfaces to be of the pointwise 1-type of the Gauss map. Finally, examples for each type of these surfaces are given, and their graphics are illustrated.</p></abstract>

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On the Framed Normal Curves in Euclidean 4-space

Cited by 3 publications

References 11 publications

Framed Curve Families Induced by Real and Complex Coupled Dispersionless-Type Equations

Framed Curve Families Induced by Real and Complex Coupled Dispersionless-Type Equations

A New Insight on Rectifying-Type Curves in Euclidean 4-Space

The developable surfaces with pointwise 1-type Gauss map of Frenet type framed base curves in Euclidean 3-space

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