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Unveiling $\: f-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms

Year 2025, Volume: 18 Issue: 1, 111 - 123, 24.04.2025

Şaban Güvenç

Abstract

In this paper, we firstly provide a concise overview of $\mathcal{S}-$manifolds, $f$-biharmonicity and $\theta _{\alpha }$-slant curves. We then derive a key equation and analyze it in detail to establish the necessary and sufficient conditions for $\theta _{\alpha }$-slant curves to be $f$-biharmonic. Finally, we present an example to support our findings.

Keywords

$\theta _{\alpha }-$slant curve $f$-biharmonic curve Frenet curve $\mathcal{S}$-space form

References

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There are 20 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Şaban Güvenç 0000-0001-6254-4693

Early Pub Date April 20, 2025
Publication Date April 24, 2025
Submission Date October 26, 2024
Acceptance Date March 2, 2025
Published in Issue Year 2025 Volume: 18 Issue: 1

Cite

APA Güvenç, Ş. (2025). Unveiling $\: f-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms. International Electronic Journal of Geometry, 18(1), 111-123.
AMA Güvenç Ş. Unveiling $\: f-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms. Int. Electron. J. Geom. April 2025;18(1):111-123.
Chicago Güvenç, Şaban. “Unveiling $\: F-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms”. International Electronic Journal of Geometry 18, no. 1 (April 2025): 111-23.
EndNote Güvenç Ş (April 1, 2025) Unveiling $\: f-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms. International Electronic Journal of Geometry 18 1 111–123.
IEEE Ş. Güvenç, “Unveiling $\: f-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms”, Int. Electron. J. Geom., vol. 18, no. 1, pp. 111–123, 2025.
ISNAD Güvenç, Şaban. “Unveiling $\: F-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms”. International Electronic Journal of Geometry 18/1 (April 2025), 111-123.
JAMA Güvenç Ş. Unveiling $\: f-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms. Int. Electron. J. Geom. 2025;18:111–123.
MLA Güvenç, Şaban. “Unveiling $\: F-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms”. International Electronic Journal of Geometry, vol. 18, no. 1, 2025, pp. 111-23.
Vancouver Güvenç Ş. Unveiling $\: f-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms. Int. Electron. J. Geom. 2025;18(1):111-23.
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