Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON SLANT CURVES IN S-MANIFOLDS

  • Guvenc, Saban (Department of Mathematics Balikesir University) ;
  • Ozgur, Cihan (Department of Mathematics Balikesir University)
  • Received : 2017.03.23
  • Accepted : 2017.11.03
  • Published : 2018.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider biharmonic slant curves in S-space forms. We obtain a main theorem, which gives us four different cases to find curvature conditions for these curves. We also give examples of slant curves in ${\mathbb{R}}^{2n+s}(-3s)$.

Keywords

References

  1. C. Baikoussis and D. E. Blair, On Legendre curves in contact 3-manifolds, Geom. Dedicata 49 (1994), no. 2, 135-142. https://doi.org/10.1007/BF01610616
  2. D. E. Blair, Geometry of manifolds with structural group $U(n){\times}O(s)$, J. Differential Geometry 4 (1970), 155-167. https://doi.org/10.4310/jdg/1214429380
  3. J. L. Cabrerizo, L. M. Fernadez, and M. Fernandez, The curvature of submanifolds of an S-space form, Acta Math. Hungar. 62 (1993), no. 3-4, 373-383. https://doi.org/10.1007/BF01874657
  4. B.-Y. Chen, A report on submanifolds of finite type, Soochow J. Math. 22 (1996), no. 2, 117-337.
  5. J. T. Cho, J. Inoguchi, and J.-E. Lee, On slant curves in Sasakian 3-manifolds, Bull. Austral. Math. Soc. 74 (2006), no. 3, 359-367. https://doi.org/10.1017/S0004972700040429
  6. J. Eells and L. Lemaire, Selected topics in harmonic maps, CBMS Regional Conference Series in Mathematics, 50, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1983.
  7. J. Eells, Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160. https://doi.org/10.2307/2373037
  8. D. Fetcu, Biharmonic Legendre curves in Sasakian space forms, J. Korean Math. Soc. 45 (2008), no. 2, 393-404. https://doi.org/10.4134/JKMS.2008.45.2.393
  9. D. Fetcu and C. Oniciuc, Explicit formulas for biharmonic submanifolds in Sasakian space forms, Pacific J. Math. 240 (2009), no. 1, 85-107. https://doi.org/10.2140/pjm.2009.240.85
  10. I. Hasegawa, Y. Okuyama, and T. Abe, On pth Sasakian manifolds, J. Hokkaido Univ. Ed. Sect. II A 37 (1986), no. 1, 1-16.
  11. G. Y. Jiang, 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A 7 (1986), no. 4, 389-402.
  12. J.-S. Kim, M. K. Dwivedi, and M. M. Tripathi, Ricci curvature of integral submanifolds of an S-space form, Bull. Korean Math. Soc. 44 (2007), no. 3, 395-406. https://doi.org/10.4134/BKMS.2007.44.3.395
  13. H. Nakagawa, On framed f-manifolds, Kodai Math. Sem. Rep. 18 (1966), 293-306. https://doi.org/10.2996/kmj/1138845274
  14. C. Ozgur and S. Guvenc, On biharmonic Legendre curves in S-space forms, Turkish J. Math. 38 (2014), no. 3, 454-461. https://doi.org/10.3906/mat-1207-8
  15. J. Vanzura, Almost r-contact structures, Ann. Scuola Norm. Sup. Pisa (3) 26 (1972), 97-115.
  16. K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3, World Scientific Publishing Co., Singapore, 1984.