Browse > Article
http://dx.doi.org/10.4134/CKMS.c170116

ON SLANT CURVES IN S-MANIFOLDS  

Guvenc, Saban (Department of Mathematics Balikesir University)
Ozgur, Cihan (Department of Mathematics Balikesir University)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.1, 2018 , pp. 293-303 More about this Journal
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
S-manifold; slant curve; biharmonic curve; Frenet curve;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 C. Baikoussis and D. E. Blair, On Legendre curves in contact 3-manifolds, Geom. Dedicata 49 (1994), no. 2, 135-142.   DOI
2 D. E. Blair, Geometry of manifolds with structural group $U(n){\times}O(s)$, J. Differential Geometry 4 (1970), 155-167.   DOI
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.   DOI
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.   DOI
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.   DOI
8 D. Fetcu, Biharmonic Legendre curves in Sasakian space forms, J. Korean Math. Soc. 45 (2008), no. 2, 393-404.   DOI
9 D. Fetcu and C. Oniciuc, Explicit formulas for biharmonic submanifolds in Sasakian space forms, Pacific J. Math. 240 (2009), no. 1, 85-107.   DOI
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.   DOI
13 H. Nakagawa, On framed f-manifolds, Kodai Math. Sem. Rep. 18 (1966), 293-306.   DOI
14 C. Ozgur and S. Guvenc, On biharmonic Legendre curves in S-space forms, Turkish J. Math. 38 (2014), no. 3, 454-461.   DOI
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.