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 R2n+s(−3s), where we choose n = 1, s = 2. Finally, we study biharmonicity of these curves in S−space forms.

___

  • Blair, D. E.: Geometry of manifolds with structural group U(n) × O(s). J. Differential Ge- ometry 4, 155-167 (1970).
  • Baikoussis, C., Blair, D. E.: On Legendre curves in contact 3-manifolds. Geom. Dedicata 49, 135–142 (1994).
  • Cabrerizo, J. L., Fernandez, L. M., Fernandez M.: The curvature of submanifolds of an S-space form. Acta Math. Hungar. 62, 373-383 (1993).
  • Chen, B.Y.: A report on submanifolds of finite type. Soochow J. Math. 22, 117-337 (1996).
  • Cho, J. T., Inoguchi, J., Lee, J.E.: On slant curves in Sasakian 3-manifolds. Bull. Austral. Math. Soc. 74, 359–367 (2006).
  • Eells, Jr. J., Lemaire, L.: Selected topics in harmonic maps. Amer. Math. Soc., Providence, R.I., (1983).
  • Eells, Jr. J., Sampson, J. H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86, 109–160 (1964).
  • Fetcu, D., Oniciuc, C.: Explicit formulas for biharmonic submanifolds in Sasakian space forms. Pacific J. Math. 240, 85-107 (2009).
  • Güvenç, Ş., Özgür, C.: On slant curves in S-manifolds. Commun. Korean Math. Soc. 33, no. 1, 293–303 (2018).
  • 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-space form. Bull. Korean Math. Soc. 44 , 395–406 (2007).
  • Nakagawa, H.: On framed f-manifolds. Kodai Math. Sem. Rep. 18, 293-306 (1966).
  • Özgür, C., Güvenç, Ş.: On biharmonic Legendre curves in S-space forms. Turkish J. Math. 38, no. 3, 454–461 (2014).
  • Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Mathematics, 3. Singapore. World Scientific Publishing Co. 1984.