An Extended Family of Slant Curves in S−manifolds

In this paper, we define an extended family of slant curves (i.e. θα−slant curves) in S−manifolds. We give two examples of such curves in R 2n+s (−3s), where we choose n = 1, s = 2. Finally, we study biharmonicity of these curves in S−space forms.

PDF

___

[1] Blair, D. E.: Geometry of manifolds with structural group U(n) × O(s). J. Differential Geometry. 4, 155-167 (1970).

[2] Baikoussis, C., Blair, D. E.: On Legendre curves in contact 3-manifolds. Geom. Dedicata. 49, 135-142 (1994).

[3] Cabrerizo, J. L., Fernandez, L. M., Fernandez M.: The curvature of submanifolds of an S-space form. Acta Math. Hungar. 62, 373-383 (1993).

[4] Chen, B.Y.: A report on submanifolds of finite type. Soochow J. Math. 22, 117-337 (1996).

[5] Cho, J. T., Inoguchi, J., Lee, J. E.: On slant curves in Sasakian 3-manifolds. Bull. Austral. Math. Soc. 74, 359-367 (2006).

[6] Eells, Jr. J., Lemaire, L.: Selected topics in harmonic maps. Amer. Math. Soc. Providence, R.I. (1983).

[7] Eells, Jr. J., Sampson, J. H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86, 109-160 (1964).

[8] Fetcu, D., Oniciuc, C.: Explicit formulas for biharmonic submanifolds in Sasakian space forms. Pacific J. Math. 240, 85-107 (2009).

[9] Güvenç, ¸S., Özgür, C.: On slant curves in S-manifolds. Commun. Korean Math. Soc. 33 (1), 293-303 (2018).

[10] Hasegawa, I., Okuyama, Y., Abe, T.: On p-th Sasakian manifolds. J. Hokkaido Univ. Ed. Sect. II A. 37 (1), 1-16 (1986).

[11] Jiang, G. Y.: 2-harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser. A. 7, 389-402 (1986).

[12] Kim, J. S., Dwivedi, M. K., Tripathi, M. M.: Ricci curvature of integral submanifolds of an S-space form. Bull. Korean Math. Soc. 44, 395-406 (2007).

[13] Nakagawa, H.: On framed f-manifolds. Kodai Math. Sem. Rep. 18, 293-306 (1966).

[14] Özgür, C., Güvenç, ¸S.: On biharmonic Legendre curves in S-space forms. Turkish J. Math. 38 (3), 454-461 (2014).

[15] Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Mathematics, 3. World Scientific Publishing Co. Singapore (1984).