f-Biminimal submanifolds of generalized space forms

Year 2019, Volume: 68 Issue: 2, 1301 - 1315, 01.08.2019

Fatma Karaca

https://doi.org/10.31801/cfsuasmas.524498

Cited By: 1

Abstract

We study f-biminimal submanifolds in generalized complex space forms and generalized Sasakian space forms. Then, we analyze f-biminimal submanifolds in these spaces. Finally, we consider f-biminimal integral submanifolds in Sasakian space forms and give an example.

Keywords

f-biminimal submanifolds, generalized complex space form, generalized Sasakian space form

References

• Alegre, P., Blair, D. E., Carriazo, A., Generalized Sasakian space forms, Israel J. Math., 141 (2004), 157--183.
• Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Boston. Birkhauser (2002).
• Course N., f-harmonic maps, PhD, University of Warwick, Coventry, CV4 7AL, UK, (2004).
• Eells, J. Jr., Sampson, J. H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86(1964), 109--160.
• Fetcu, D., Loubeau, E., Montaldo, S., Oniciuc, C., Biharmonic submanifolds of CPⁿ, Math. Z., 266 (2010), 505 -- 531.
• Fetcu, D., Oniciuc, C., Explicit formulas for biharmonic submanifolds in Sasakian space forms, Pacific J. Math. 240 (2009), no. 1, 85--107.
• Gürler F., Özgür C., f-Biminimal immersions, Turkish J. Math., 41 (2017), 564--575.
• Jiang, G.Y., 2-Harmonic maps and their first and second variational formulas, Chinese Ann. Math., Ser. A 7(1986), 389--402.
• Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93--103.
• Lotta, A., Slant submanifolds in contact geometry, Bull. Math. Soc. Roumanie, 39 (1996), 183-198.
• Loubeau, L., Montaldo S., Biminimal immersions, Proc. Edinb. Math. Soc., 51 (2008), 421-437.
• Lu,W-J., On f-bi-harmonic maps and bi-f-harmonic maps between Riemannian manifolds, Science China Math. 58 (2015), 1483-1498.
• Ludden, G.D., Submanifolds of cosymplectic manifolds, J. Differential Geometry, 4 (1970) 237--244.
• Olszak, Z., On the existence of generalized complex space forms, Israel J. Math., 65 (1989), no. 2, 214 -- 218.
• Ouakkas S., Nasri R., Djaa M., On the f-harmonic and f-biharmonic maps. JP. J. Geom. Top. (1), 10 (2010), 11--27.
• Ou Y-L., On f-biharmonic maps and f-biharmonic submanifolds, Pacific J. Math., 271 (2014), 461--477.
• Roth, J., Upadhyay, A., Biharmonic submanifolds of generalized space forms, Diff. Geo. and Appl. 50 (2017), 88-104.
• Roth, J., Upadhyay, A., f-Biharmonic and Bi-f-harmonic submanifolds of generalized space forms, arXiv:1609.08599 (2017).
• Tricerri, F., Vanhecke, L., Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc., 267 (1981), no. 2, 365 -- 397.
• Yano, K., Kon, M., Structures on manifolds, Series in Pure Mathematics. Singapore: World Scientific Publishing Co., (1984).