Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms

Şerife Nur Bozdağ; Selcen Yüksel Perktaş; Feyza Esra Erdoğan

doi:10.53570/jnt.1508392

EN

Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms

Abstract

In this study, we consider bi-$f$-harmonic Legendre curves on $(\alpha,\beta)$-trans-Sasakian generalized Sasakian space form. We provide the necessary and sufficient conditions for a Legendre curve to be bi-$f$-harmonic on $(\alpha,\beta)$-trans-Sasakian generalized Sasakian space form without any restrictions by a main theorem. Afterward, we investigate these conditions under nine different cases. As a result of these investigations, we obtain the original theorems and corollaries as well as the nonexistence theorems. We perform these investigations according to the $\rho_{2}$ and $\rho_{3}$ functions from the curvature tensor of the $(\alpha,\beta)$-trans-Sasakian generalized Sasakian space form, the curvature and torsion of the bi-$f$-harmonic Legendre curve, and finally, the positions of the basis vectors relative to each other.

Keywords

Bi-$f$-harmonic curves, Legendre curves, trans-Sasakian space forms, generalized Sasakian space forms

References

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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Şerife Nur Bozdağ ^*
0000-0002-9651-7834
Türkiye

Selcen Yüksel Perktaş
0000-0002-8848-0621
Türkiye

Feyza Esra Erdoğan
0000-0003-0568-7510
Türkiye

Publication Date

September 30, 2024

Submission Date

July 1, 2024

Acceptance Date

September 14, 2024

Published in Issue

Year 2024 Number: 48

DOI

https://doi.org/10.53570/jnt.1508392

IZ

https://izlik.org/JA49NW97NZ

APA

Bozdağ, Ş. N., Yüksel Perktaş, S., & Erdoğan, F. E. (2024). Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms. Journal of New Theory, 48, 24-39. https://doi.org/10.53570/jnt.1508392

AMA

1.Bozdağ ŞN, Yüksel Perktaş S, Erdoğan FE. Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms. JNT. 2024;(48):24-39. doi:10.53570/jnt.1508392

Chicago

Bozdağ, Şerife Nur, Selcen Yüksel Perktaş, and Feyza Esra Erdoğan. 2024. “Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms”. Journal of New Theory, nos. 48: 24-39. https://doi.org/10.53570/jnt.1508392.

EndNote

Bozdağ ŞN, Yüksel Perktaş S, Erdoğan FE (September 1, 2024) Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms. Journal of New Theory 48 24–39.

IEEE

[1]Ş. N. Bozdağ, S. Yüksel Perktaş, and F. E. Erdoğan, “Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms”, JNT, no. 48, pp. 24–39, Sept. 2024, doi: 10.53570/jnt.1508392.

ISNAD

Bozdağ, Şerife Nur - Yüksel Perktaş, Selcen - Erdoğan, Feyza Esra. “Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms”. Journal of New Theory. 48 (September 1, 2024): 24-39. https://doi.org/10.53570/jnt.1508392.

JAMA

1.Bozdağ ŞN, Yüksel Perktaş S, Erdoğan FE. Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms. JNT. 2024;:24–39.

MLA

Bozdağ, Şerife Nur, et al. “Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms”. Journal of New Theory, no. 48, Sept. 2024, pp. 24-39, doi:10.53570/jnt.1508392.

Vancouver

1.Şerife Nur Bozdağ, Selcen Yüksel Perktaş, Feyza Esra Erdoğan. Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms. JNT. 2024 Sep. 1;(48):24-39. doi:10.53570/jnt.1508392