Year 2020, Volume 8 , Issue 1, Pages 69 - 77 2020-03-20

An Extended Family of Slant Curves in S −manifolds

Şaban GÜVENÇ [1]


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.
θα−slant curve, S−manifold, biharmonic curve
  • 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.
Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Author: Şaban GÜVENÇ
Institution: Balıkesir Üniversitesi
Country: Turkey


Dates

Publication Date : March 20, 2020

Bibtex @research article { mathenot661351, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2020}, volume = {8}, pages = {69 - 77}, doi = {10.36753/mathenot.661351}, title = {An Extended Family of Slant Curves in S −manifolds}, key = {cite}, author = {GÜVENÇ, Şaban} }
APA GÜVENÇ, Ş . (2020). An Extended Family of Slant Curves in S −manifolds. Mathematical Sciences and Applications E-Notes , 8 (1) , 69-77 . DOI: 10.36753/mathenot.661351
MLA GÜVENÇ, Ş . "An Extended Family of Slant Curves in S −manifolds". Mathematical Sciences and Applications E-Notes 8 (2020 ): 69-77 <https://dergipark.org.tr/en/pub/mathenot/issue/53229/661351>
Chicago GÜVENÇ, Ş . "An Extended Family of Slant Curves in S −manifolds". Mathematical Sciences and Applications E-Notes 8 (2020 ): 69-77
RIS TY - JOUR T1 - An Extended Family of Slant Curves in S −manifolds AU - Şaban GÜVENÇ Y1 - 2020 PY - 2020 N1 - doi: 10.36753/mathenot.661351 DO - 10.36753/mathenot.661351 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 69 EP - 77 VL - 8 IS - 1 SN - -2147-6268 M3 - doi: 10.36753/mathenot.661351 UR - https://doi.org/10.36753/mathenot.661351 Y2 - 2020 ER -
EndNote %0 Mathematical Sciences and Applications E-Notes An Extended Family of Slant Curves in S −manifolds %A Şaban GÜVENÇ %T An Extended Family of Slant Curves in S −manifolds %D 2020 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 8 %N 1 %R doi: 10.36753/mathenot.661351 %U 10.36753/mathenot.661351
ISNAD GÜVENÇ, Şaban . "An Extended Family of Slant Curves in S −manifolds". Mathematical Sciences and Applications E-Notes 8 / 1 (March 2020): 69-77 . https://doi.org/10.36753/mathenot.661351
AMA GÜVENÇ Ş . An Extended Family of Slant Curves in S −manifolds. Math. Sci. Appl. E-Notes. 2020; 8(1): 69-77.
Vancouver GÜVENÇ Ş . An Extended Family of Slant Curves in S −manifolds. Mathematical Sciences and Applications E-Notes. 2020; 8(1): 77-69.