Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection

Ashis Mondal

doi:10.47000/tjmcs.1828159

Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection

Abstract

In this paper, we study biharmonic Legendre curves and slant curve in a three-dimensional $f$-Kenmotsu manifold with respect to semi-symmetric metric connection. We find curvature and torsion of Legendre curve in a three-dimensional $f$-Kenmotsu manifold with respect to semi-symmetric metric connection. Also, we study $C-$parallel and $C-$proper mean curvature vector fields in the tangent and normal bundles in a three-dimensional $f$-Kenmotsu manifold with respect to semi-symmetric metric connection.

Keywords

References

Baikoussis, C., Blair, D.E., On Legendre curves in contact 3-manifolds, Geometry Dedicata, 49(1994), 135–142.
Cho, J.T., Lee, J.E., Slant curves in contact pseudo-Hermitian manifolds, Bull. Austral. Math. Soc., 78(2008), 383–396.
Cho, J.T., Inoguchi, J., Lee, J.E., On slant curves in Sasakian 3-manifolds, Bull. Austral. Math. Soc., 74(2006), 359–367.
De, U.C., Biswas, S.C., On a type of semi-symmetric metric connection on a Riemannian manifold, Pub. De L Institut Math., N. S., Tome, 61(1997), 90–96.
Eells, J., Sampson, J.H., Harmonic mapping of the Riemannian manifold, American J. Math., 86(1964), 109—160.
Friedmann, A., Schouten, J.A., Uber die Geometric derhalbsymmetrischen Ubertragung, Math., Zeitschr., 21(1924), 211–223.
Güvenc, Ş., Özgür, Ç., On slant curves in trans-Sasakian manifolds, Rev. Un. Mat. Argentina., 55(2014), 81–100.
Hayden, H.A., Subspaces of space with torsion, Proc. London Math. Soc., 34(1932), 27–50.

Haseeb, A., Prasad, R., On a class of 3-dimensional f -Kenmotsu manifolds, Bull. Trans. Univ. of Brasov, Series III: Mathematics, Informatics, Physics, 11(60), 2(2019), 109–118.
Inoguchi, J.I., Biharmonic curves in Minkowski 3-space, International J. of Math. and Math. Sciences, 21(2003), 1365–1368.
Inoguchi, J., Lee, J.E., Slant curves in 3-dimensional almost contact metric geometry, Int. Electron. J. Geom. 8(2015), 106–146.
Inoguchi, J., Lee, J.E., Affine biharmonic curves in 3-dimensional homogenious geometries, Mediterr. J. Math., 10(2013), 571–592.
Jiang, G.Y., 2- harmonic maps and their first and second variation formulas, Chinese Ann. Math. Ser. A., 7(1986), 389—402.
Janssens, D., Vanheck, L., Almost contact structures and curvature tensors, Kodai Math. J., 4(1981), 1–27.
Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku math. J., 24(1972), 93–103.
Kazan, A., Karadaˇg, H.B., Trans-Sasakian manifolds with Schouten-Van Kampen connection, Ilirias J. of Math., 7(2018), 1–12.
Lee, J.E., Suh, Y.J., Lee, H., C-parallel mean curvature vector fields along slant curves in Sasakian 3-manifolds, Kyungpook Math. J., 52(2012), 49–59.
Lee, J.E., On Legendre curves in contact pseudo-Hermitian 3-manifolds, Bull. Aust. Math. Soc., 81(2010), 156–164.
Mondal, A., Legendre curves on 3-dimensional f -Kenmotsu manifolds admitting Schouten-Van Kampen connection, Facta Univ.(Nis), Ser. Math. Inform., 35(2020), 357–366.
Özgür, C., Güvenc, S., On biharmonic Legendre curves in S-space forms, Turkish J. Math., 38(2014), 454–461.
Olszak, Z., Locally conformal almost cosymplectic manifolds, Colloq. Math., 57(1989), 73–87.
Olszak, Z., Rosca, R., Normal locally conformal almost cosymplectice manifolds, Publ. Math., 39(1991), 315–323.
Olszak, Z., The Schouten-Van Kampen affine connection adapted to an almost(para) contact metric structure, Publications Delinstitut Mathematique, 94(2013), 31–42.
Prasad, R., Haseeb, A., Gautam, U.K., On three dimensional f -Kenmotsu manifolds with a certain connection, Glob. J. of Advt. Res. on Class. and Modern Geom., 10(2021), 91–101.
Sarkar, A., Mondal, A., Biswas, D., Some curves on three-dimensional trans-Sasakian manifolds with semi-symmetric metric connection, Palestine J. of Math., 5(2016), 195–203.
Sarkar, A., Hui, S.K., Sen, M., A study on Legendre curves in three dimensional trans-Sasakian manifold, Lobachevskii J. Math., 35(2014), 11–18.
Tang, W., Majhi, P., Zhao, P., De, U.C., Legendre curves on 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection, Filomat 32(2018), 3651–3656.
Welyczko, J., On Legendre curves in 3-dimensional normal almost contact metric manifolds, Soochow J. Math., 33(2007), 929–937.
Welyczko, J., Slant curves in 3-dimensional normal almost paracontact metric manifolds, Mediterr. J. Math., 11(2014), 965–978.
Yadav, S.K., Yildiz, A., Q-Curvature Tensor on f-Kenmotsu 3-Manifolds, Universal Journal of Mathematics and Applications, 5(2022), 96–106.
Yildiz, A., De, U.C., Turan, M., On 3-Dimensional f -Kenmotsu manifold and Ricci solition, Ukrainian Math. J., 65(2013), 684–693.
Yano, K., On semi-symmetric metric connection, Rev. Roum. Math. Pures. Appl., 15(1970), 1579–1586.

Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Ashis Mondal ^*
0000-0003-3668-593X
India

Publication Date

October 13, 2026

Submission Date

November 22, 2025

Acceptance Date

April 17, 2026

Published in Issue

Year 2026 Volume: 18 Number: 3

DOI

https://doi.org/10.47000/tjmcs.1828159

IZ

https://izlik.org/JA88BA95ZA

Cite

RIS / Bibtex

APA

Mondal, A. (2026). Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection. Turkish Journal of Mathematics and Computer Science, 18(3), 836-847. https://doi.org/10.47000/tjmcs.1828159

AMA

1.Mondal A. Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection. TJMCS. 2026;18(3):836-847. doi:10.47000/tjmcs.1828159

Chicago

Mondal, Ashis. 2026. “Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection”. Turkish Journal of Mathematics and Computer Science 18 (3): 836-47. https://doi.org/10.47000/tjmcs.1828159.

EndNote

Mondal A (October 1, 2026) Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection. Turkish Journal of Mathematics and Computer Science 18 3 836–847.

IEEE

[1]A. Mondal, “Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection”, TJMCS, vol. 18, no. 3, pp. 836–847, Oct. 2026, doi: 10.47000/tjmcs.1828159.

ISNAD

Mondal, Ashis. “Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection”. Turkish Journal of Mathematics and Computer Science 18/3 (October 1, 2026): 836-847. https://doi.org/10.47000/tjmcs.1828159.

JAMA

1.Mondal A. Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection. TJMCS. 2026;18:836–847.

MLA

Mondal, Ashis. “Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 3, Oct. 2026, pp. 836-47, doi:10.47000/tjmcs.1828159.

Vancouver

1.Ashis Mondal. Certain Curves in $f$-Kenmotsu 3-Manifolds Admitting Semi-Symmetric Metric Connection. TJMCS. 2026 Oct. 1;18(3):836-47. doi:10.47000/tjmcs.1828159