KaydedilenlerDerginizi ekleyin

Dergiler / International Electronic Journal of Geometry / 2019 / Volume: 12 Issue: 2

A Note on f-biharmonic Legendre Curves in S-Space Forms

Şaban Güvenç(BALIKESİR ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0001-6254-4693
Sayfa
—
Yayın Tarihi
2019-10-03
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also give a proper example of f-biharmonic Legendre curves in the S-space form R^(2m+s)(−3s), with m = 2 and s = 2.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we study f-biharmonic Legendre curves in S-space forms.
📊
Temel Bulgular & Veri:Our aim is to find curvature conditions for these curves and determine their types, i.e., a geodesic, a circle, a helix or a Frenet curve of osculating order r with specific curvature equations.
💡
Sonuç & Katkı:We also give a proper example of f-biharmonic Legendre curves in the S-space form R^(2m+s)(−3s), with m = 2 and s = 2.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:S−space form · Legendre curve · f-biharmonic curve

Abstract

In this paper, we study f-biharmonic Legendre curves in S-space forms. Our aim is to find curvature conditions for these curves and determine their types, i.e., a geodesic, a circle, a helix or a Frenet curve of osculating order r with specific curvature equations. We also give a proper example of f-biharmonic Legendre curves in the S-space form R^(2m+s)(−3s), with m = 2 and s = 2.

🔖

Bu Makaleye Atıf Yap

Güvenç, Ş. (2019). A Note on f-biharmonic Legendre Curves in S-Space Forms. International Electronic Journal of Geometry, Volume: 12 Issue: 2. https://doi.org/10.36890/iejg.554662

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (22)

  1. Blair, D. E.: Geometry of manifolds with structural group U(n) × O(s). J. Differential Geometry 4,155-167 (1970).
  2. Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. Boston. Birkhauser 2002.
  3. Cabrerizo, J. L., Fernandez, L. M., Fernandez M.: The curvature of submanifolds of an S-space form.Acta Math. Hungar. 62, 373-383 (1993).
  4. Caddeo, R., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds of S3. Internat. J. Math. 12, 867-876(2001).
  5. Caddeo, R., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds in spheres. Israel J. Math. 130, 109-123(2002).
  6. Chen, B.Y.: A report on submanifolds of finite type. Soochow J. Math. 22, 117-337 (1996).
  7. Eells, Jr. J., Sampson, J. H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86, 109–160(1964).
  8. Fetcu, D.: Biharmonic Legendre curves in Sasakian space forms. J. Korean Math. Soc. 45, 393-404(2008).
  9. Fetcu, D., Oniciuc, C.: Explicit formulas for biharmonic submanifolds in Sasakian space forms. PacificJ. Math. 240, 85-107 (2009).
  10. Fetcu, D., Loubeau, E., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds of CPn. Math. Z. 266,505–531 (2010).
  11. Güvenç, ޸. Özgür, C.: On the characterizations of f-biharmonic Legendre curves in Sasakian spaceforms. Filomat 31, no. 3, 639–648 (2017).
  12. Hasegawa, I., Okuyama, Y., Abe, T.: On p-th Sasakian manifolds. J. Hokkaido Univ. Ed. Sect. II A,37, no. 1, 1–16, (1986).
  13. Jiang, G. Y.: 2-harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser.A, 7, 389-402 (1986).
  14. Kim, J. S., Dwivedi, M. K., Tripathi, M. M.: Ricci curvature of integral submanifolds of an S-spaceform. Bull. Korean Math. Soc. 44, 395–406 (2007).
  15. Lu, W. J.: On f-biharmonic maps between Riemannian manifolds. arXiv:1305.5478 (2013).
  16. Nakagawa, H.: On framed f-manifolds. Kodai Math. Sem. Rep. 18, 293-306 (1966).
  17. Ou, Y.L.: On f-biharmonic maps and f-biharmonic submanifolds. arXiv:1306.3549v1.
  18. Ou, Y.L.: p-Harmonic morphisms, biharmonic morphisms,and nonharmonic biharmonic maps. J. Geom.Phys. 56, 358-374 (2006).
  19. Özgür, C., Güvenç, ޸.: On Biharmonic Legendre Curves in S-Space Forms. Turkish Journal of Mathematics,Turk. J. Math. 38 (2014), 454-461.
  20. Vanzura, J.: Almost r-contact structures. Ann. Scuola Norm. Sup. Pisa (3) 26, 97-115 (1972).
  21. Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Mathematics, 3. Singapore. World ScientificPublishing Co. 1984.
  22. Kim, J. S., Dwivedi, M. K., Tripathi, M. M.: Ricci curvature of integral submanifolds of an S-spaceform. Bull. Korean Math. Soc. 44, 395–406 (2007).