A Note on f-biharmonic Legendre Curves in S-Space Forms
In this paper, we study f-biharmonic Legendre curves in S-space forms. Our aim is to find curvature conditions for these curves and determine their types, i.e., a geodesic, a circle, a helix or a Frenet curve of osculating order r with specific curvature equations. We also give a proper example of f-biharmonic Legendre curves in the S-space form R^(2m+s)(−3s), with m = 2 and s = 2.
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- Blair, D. E.: Geometry of manifolds with structural group U(n) × O(s). J. Differential Geometry 4,155-167 (1970).
- Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. Boston. Birkhauser 2002.
- Cabrerizo, J. L., Fernandez, L. M., Fernandez M.: The curvature of submanifolds of an S-space form.Acta Math. Hungar. 62, 373-383 (1993).
- Caddeo, R., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds of S3. Internat. J. Math. 12, 867-876(2001).
- Caddeo, R., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds in spheres. Israel J. Math. 130, 109-123(2002).
- Chen, B.Y.: A report on submanifolds of finite type. Soochow J. Math. 22, 117-337 (1996).
- Eells, Jr. J., Sampson, J. H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86, 109–160(1964).
- Fetcu, D.: Biharmonic Legendre curves in Sasakian space forms. J. Korean Math. Soc. 45, 393-404(2008).
- Fetcu, D., Oniciuc, C.: Explicit formulas for biharmonic submanifolds in Sasakian space forms. PacificJ. Math. 240, 85-107 (2009).
- Fetcu, D., Loubeau, E., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds of CPn. Math. Z. 266,505–531 (2010).
- Güvenç, ޸. Özgür, C.: On the characterizations of f-biharmonic Legendre curves in Sasakian spaceforms. Filomat 31, no. 3, 639–648 (2017).
- Hasegawa, I., Okuyama, Y., Abe, T.: On p-th Sasakian manifolds. J. Hokkaido Univ. Ed. Sect. II A,37, no. 1, 1–16, (1986).
- Jiang, G. Y.: 2-harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser.A, 7, 389-402 (1986).
- Kim, J. S., Dwivedi, M. K., Tripathi, M. M.: Ricci curvature of integral submanifolds of an S-spaceform. Bull. Korean Math. Soc. 44 , 395–406 (2007).
- Lu, W. J.: On f-biharmonic maps between Riemannian manifolds. arXiv:1305.5478 (2013).
- Nakagawa, H.: On framed f-manifolds. Kodai Math. Sem. Rep. 18, 293-306 (1966).
- Ou, Y.L.: On f-biharmonic maps and f-biharmonic submanifolds. arXiv:1306.3549v1.
- Ou, Y.L.: p-Harmonic morphisms, biharmonic morphisms,and nonharmonic biharmonic maps. J. Geom.Phys. 56, 358-374 (2006).
- Özgür, C., Güvenç, ޸.: On Biharmonic Legendre Curves in S-Space Forms. Turkish Journal of Mathematics,Turk. J. Math. 38 (2014), 454-461.
- Vanzura, J.: Almost r-contact structures. Ann. Scuola Norm. Sup. Pisa (3) 26, 97-115 (1972).
- Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Mathematics, 3. Singapore. World ScientificPublishing Co. 1984.