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

Yıl 2019, Cilt: 12 Sayı: 2, 260 - 267, 03.10.2019
https://doi.org/10.36890/iejg.554662

Öz

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.

Kaynakça

  • Blair, D. E.: Geometry of manifolds with structural group U(n) × O(s). J. Differential Geometry 4,155-167 (1970).
  • Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. Boston. Birkhauser 2002.
  • Cabrerizo, J. L., Fernandez, L. M., Fernandez M.: The curvature of submanifolds of an S-space form.Acta Math. Hungar. 62, 373-383 (1993).
  • Caddeo, R., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds of S3. Internat. J. Math. 12, 867-876(2001).
  • Caddeo, R., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds in spheres. Israel J. Math. 130, 109-123(2002).
  • Chen, B.Y.: A report on submanifolds of finite type. Soochow J. Math. 22, 117-337 (1996).
  • Eells, Jr. J., Sampson, J. H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86, 109–160(1964).
  • Fetcu, D.: Biharmonic Legendre curves in Sasakian space forms. J. Korean Math. Soc. 45, 393-404(2008).
  • Fetcu, D., Oniciuc, C.: Explicit formulas for biharmonic submanifolds in Sasakian space forms. PacificJ. Math. 240, 85-107 (2009).
  • Fetcu, D., Loubeau, E., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds of CPn. Math. Z. 266,505–531 (2010).
  • Güvenç, ޸. Özgür, C.: On the characterizations of f-biharmonic Legendre curves in Sasakian spaceforms. Filomat 31, no. 3, 639–648 (2017).
  • 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-spaceform. Bull. Korean Math. Soc. 44 , 395–406 (2007).
  • Lu, W. J.: On f-biharmonic maps between Riemannian manifolds. arXiv:1305.5478 (2013).
  • Nakagawa, H.: On framed f-manifolds. Kodai Math. Sem. Rep. 18, 293-306 (1966).
  • Ou, Y.L.: On f-biharmonic maps and f-biharmonic submanifolds. arXiv:1306.3549v1.
  • Ou, Y.L.: p-Harmonic morphisms, biharmonic morphisms,and nonharmonic biharmonic maps. J. Geom.Phys. 56, 358-374 (2006).
  • Özgür, C., Güvenç, ޸.: On Biharmonic Legendre Curves in S-Space Forms. Turkish Journal of Mathematics,Turk. J. Math. 38 (2014), 454-461.
  • Vanzura, J.: Almost r-contact structures. Ann. Scuola Norm. Sup. Pisa (3) 26, 97-115 (1972).
  • Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Mathematics, 3. Singapore. World ScientificPublishing Co. 1984.
Yıl 2019, Cilt: 12 Sayı: 2, 260 - 267, 03.10.2019
https://doi.org/10.36890/iejg.554662

Öz

Kaynakça

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

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Şaban Güvenç 0000-0001-6254-4693

Yayımlanma Tarihi 3 Ekim 2019
Kabul Tarihi 10 Eylül 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 2

Kaynak Göster

APA Güvenç, Ş. (2019). A Note on f-biharmonic Legendre Curves in S-Space Forms. International Electronic Journal of Geometry, 12(2), 260-267. https://doi.org/10.36890/iejg.554662
AMA Güvenç Ş. A Note on f-biharmonic Legendre Curves in S-Space Forms. Int. Electron. J. Geom. Ekim 2019;12(2):260-267. doi:10.36890/iejg.554662
Chicago Güvenç, Şaban. “A Note on F-Biharmonic Legendre Curves in S-Space Forms”. International Electronic Journal of Geometry 12, sy. 2 (Ekim 2019): 260-67. https://doi.org/10.36890/iejg.554662.
EndNote Güvenç Ş (01 Ekim 2019) A Note on f-biharmonic Legendre Curves in S-Space Forms. International Electronic Journal of Geometry 12 2 260–267.
IEEE Ş. Güvenç, “A Note on f-biharmonic Legendre Curves in S-Space Forms”, Int. Electron. J. Geom., c. 12, sy. 2, ss. 260–267, 2019, doi: 10.36890/iejg.554662.
ISNAD Güvenç, Şaban. “A Note on F-Biharmonic Legendre Curves in S-Space Forms”. International Electronic Journal of Geometry 12/2 (Ekim 2019), 260-267. https://doi.org/10.36890/iejg.554662.
JAMA Güvenç Ş. A Note on f-biharmonic Legendre Curves in S-Space Forms. Int. Electron. J. Geom. 2019;12:260–267.
MLA Güvenç, Şaban. “A Note on F-Biharmonic Legendre Curves in S-Space Forms”. International Electronic Journal of Geometry, c. 12, sy. 2, 2019, ss. 260-7, doi:10.36890/iejg.554662.
Vancouver Güvenç Ş. A Note on f-biharmonic Legendre Curves in S-Space Forms. Int. Electron. J. Geom. 2019;12(2):260-7.