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Year 2020, Volume: 8 Issue: 1, 69 - 77, 20.03.2020
https://doi.org/10.36753/mathenot.661351

Abstract

References

  • 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).
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  • 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.

An Extended Family of Slant Curves in S −manifolds

Year 2020, Volume: 8 Issue: 1, 69 - 77, 20.03.2020
https://doi.org/10.36753/mathenot.661351

Abstract

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.

References

  • 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.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Şaban Güvenç

Publication Date March 20, 2020
Submission Date December 18, 2019
Acceptance Date February 14, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Güvenç, Ş. (2020). An Extended Family of Slant Curves in S −manifolds. Mathematical Sciences and Applications E-Notes, 8(1), 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. March 2020;8(1):69-77. doi:10.36753/mathenot.661351
Chicago Güvenç, Şaban. “An Extended Family of Slant Curves in S −manifolds”. Mathematical Sciences and Applications E-Notes 8, no. 1 (March 2020): 69-77. https://doi.org/10.36753/mathenot.661351.
EndNote Güvenç Ş (March 1, 2020) An Extended Family of Slant Curves in S −manifolds. Mathematical Sciences and Applications E-Notes 8 1 69–77.
IEEE Ş. Güvenç, “An Extended Family of Slant Curves in S −manifolds”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 69–77, 2020, doi: 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.
JAMA Güvenç Ş. An Extended Family of Slant Curves in S −manifolds. Math. Sci. Appl. E-Notes. 2020;8:69–77.
MLA Güvenç, Şaban. “An Extended Family of Slant Curves in S −manifolds”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, 2020, pp. 69-77, doi:10.36753/mathenot.661351.
Vancouver Güvenç Ş. An Extended Family of Slant Curves in S −manifolds. Math. Sci. Appl. E-Notes. 2020;8(1):69-77.

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