On Bi-f-Harmonic Legendre Curves in Sasakian Space Forms

Year 2022, , 132 - 145, 28.07.2022

Şerife Nur Bozdağ

https://doi.org/10.54974/fcmathsci.1055588

Cited By: 1

Abstract

In this study, we consider bi-f -harmonic Legendre curves in Sasakian space forms. We
investigate necessary and sufficient conditions for a Legendre curve to be bi-f -harmonic in various cases.

Keywords

Bi-$f$-harmonic Curves, Legendre Curves, Sasakian Space Forms

References

• Baird P., Wood J.C., Harmonic Morphisms between Riemannain Manifolds, Oxford Sciences Publications, 2003.
• Blair D.E., Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, 2002.
• Eells J., Sampson J.H., Harmonic mappings of Riemannian manifolds, American Journal of Mathematics, 86, 109-160, 1964.
• Fetcu D., Biharmonic Legendre curves in Sasakian space forms, Journal of Korean Mathematical Society, 45, 393-404, 2008.
• Fetcu D., Oniciuc C., Explicit formulas for biharmonic submanifolds in Sasakian space forms, Pacific Journal of Mathematics, 240, 85-107, 2009.
• Güvenç Ş., A note on f-biharmonic Legendre curves in S-space forms, International Electronic Journal of Geometry, 12(2), 260-267, 2019.
• Güvenç Ş., Özgür C., On the characterizations of f-biharmonic Legendre Curves in Sasakian space forms, Filomat, 31(3), 639-648, 2017.
• Maeta S., k -harmonic maps into a Riemannian manifold with constant sectional curvature, Proceedings of the American Mathematical Society, 140, 1835-1847, 2012.
• Ouakkas S., Nasri R., Djaa M., On the f-harmonic and f-biharmonic maps, JP Journal of Geometry and Topology, 10(1), 11-27, 2010.
• Özgür C., Güvenç Ş., On some classes of biharmonic Legendre curves in generalized Sasakian space forms, Collectanea Mathematica, 65, 203-218, 2014.
• Özgür C., Güvenç Ş., On biharmonic Legendre curves in S-space forms, Turkish Journal of Mathematics, 38, 454-461, 2014.
• Perktaş S.Y., Blaga A.M., Erdoğan F.E., Acet B.E., Bi-f-harmonic curves and hypersurfaces, Filomat, 33(16), 5167-5180, 2019.
• Yano K., Kon M., Structures on Manifolds: Series in Pure Mathematics, World Scientific Publishing Co., 1984.
• Zhao C.L., Lu W.J., Bi-f-harmonic map equations on singly warped product manifolds, Applied Mathematics-A Journal of Chinese Universities, 30(1), 111-126, 2015.