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On f-Biharmonic Curves

Year 2018, Volume: 11 Issue: 2, 18 - 27, 30.11.2018
https://doi.org/10.36890/iejg.545115

Abstract

We study f-biharmonic curves in Sol spaces, Cartan-Vranceanu 3-dimensional spaces,
homogeneous contact 3-manifolds and we analyze non-geodesic f-biharmonic curves in these
spaces.

References

  • [1] Blair, D. E., Riemannian Geometry of Contact and Symplectic Manifolds. Boston. Birkhauser 2002.
  • [2] Caddeo, R., Montaldo, S. and Oniciuc, C., Biharmonic submanifolds of S3. Internat. J. Math. 12 (2001), 867-876.
  • [3] Caddeo, R., Montaldo, S. and Oniciuc, C., Biharmonic submanifolds in spheres. Israel J. Math. 130 (2002), 109-123.
  • [4] Caddeo, R., Montaldo, S. and Piu, P., Biharmonic curves on a surface. Rend. Mat. Appl. 21 (2001), 143-157.
  • [5] Caddeo, R., Montaldo, S., Oniciuc, C. and Piu, P., The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional spaces. The 7th Int. Workshop on Dif. Geo. and its Appl. 121-131, Cluj Univ. Press, Cluj-Napoca, 2006.
  • [6] Course, N., f-harmonic maps. Ph.D thesis, University of Warwick, Coventry, (2004) CV4 7AL, UK.
  • [7] Caddeo, R., Oniciuc, C. and Piu, P., Explicit formulas for non-geodesic biharmonic curves of the Heisenberg group. Rend. Sem. Mat. Univ. Politec. Torino. 62 (2004), 265-277.
  • [8] Eells, J. Jr. and Sampson, J. H., Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86 (1964), 109-160.
  • [9] Güvenç, ¸S. and Özgür, C., On the characterizations of f-biharmonic Legendre curves in Sasakian space forms. Filomat. 31 (2017), 639-648.
  • [10] Inoguchi, J., Biminimal submanifolds in contact 3-manifolds. Balkan J. Geom. Appl. 12 (2007), 56-67.
  • [11] Jiang, G. Y., 2-Harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser. A. 7 (1986), 389-402.
  • [12] Lu,W-J., On f-Biharmonic maps and bi-f-harmonic maps between Riemannian manifolds. Sci. China Math. 58 (2015), 1483-1498.
  • [13] Ouakkas, S., Nasri,R. and Djaa, M., On the f-harmonic and f-biharmonic maps. JP Journal of Geom. and Top. 10 (2010), 11-27. [14] Ou, Y-L., On f-biharmonic maps and f-biharmonic submanifolds. Pacific J. Math. 271 (2014), 461-477.
  • [15] Ou, Y-L. and Wang, Z-P., Biharmonic maps into Sol and Nil spaces. arXiv preprint math/0612329 (2006).
  • [16] Ou, Y-L. and Wang, Z-P., Linear biharmonic maps into Sol, Nil and Heisenberg spaces. Mediterr. J. Math. 5 (2008), 379-394.
  • [17] Perrone, D., Homogeneous contact Riemannian three-manifolds. Illinois J. Math. 42 (1998), 243-256.
  • [18] Troyanov-EPFL, M., L’horizon de SOL. Exposition. Math. 16 (1998).
Year 2018, Volume: 11 Issue: 2, 18 - 27, 30.11.2018
https://doi.org/10.36890/iejg.545115

Abstract

References

  • [1] Blair, D. E., Riemannian Geometry of Contact and Symplectic Manifolds. Boston. Birkhauser 2002.
  • [2] Caddeo, R., Montaldo, S. and Oniciuc, C., Biharmonic submanifolds of S3. Internat. J. Math. 12 (2001), 867-876.
  • [3] Caddeo, R., Montaldo, S. and Oniciuc, C., Biharmonic submanifolds in spheres. Israel J. Math. 130 (2002), 109-123.
  • [4] Caddeo, R., Montaldo, S. and Piu, P., Biharmonic curves on a surface. Rend. Mat. Appl. 21 (2001), 143-157.
  • [5] Caddeo, R., Montaldo, S., Oniciuc, C. and Piu, P., The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional spaces. The 7th Int. Workshop on Dif. Geo. and its Appl. 121-131, Cluj Univ. Press, Cluj-Napoca, 2006.
  • [6] Course, N., f-harmonic maps. Ph.D thesis, University of Warwick, Coventry, (2004) CV4 7AL, UK.
  • [7] Caddeo, R., Oniciuc, C. and Piu, P., Explicit formulas for non-geodesic biharmonic curves of the Heisenberg group. Rend. Sem. Mat. Univ. Politec. Torino. 62 (2004), 265-277.
  • [8] Eells, J. Jr. and Sampson, J. H., Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86 (1964), 109-160.
  • [9] Güvenç, ¸S. and Özgür, C., On the characterizations of f-biharmonic Legendre curves in Sasakian space forms. Filomat. 31 (2017), 639-648.
  • [10] Inoguchi, J., Biminimal submanifolds in contact 3-manifolds. Balkan J. Geom. Appl. 12 (2007), 56-67.
  • [11] Jiang, G. Y., 2-Harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser. A. 7 (1986), 389-402.
  • [12] Lu,W-J., On f-Biharmonic maps and bi-f-harmonic maps between Riemannian manifolds. Sci. China Math. 58 (2015), 1483-1498.
  • [13] Ouakkas, S., Nasri,R. and Djaa, M., On the f-harmonic and f-biharmonic maps. JP Journal of Geom. and Top. 10 (2010), 11-27. [14] Ou, Y-L., On f-biharmonic maps and f-biharmonic submanifolds. Pacific J. Math. 271 (2014), 461-477.
  • [15] Ou, Y-L. and Wang, Z-P., Biharmonic maps into Sol and Nil spaces. arXiv preprint math/0612329 (2006).
  • [16] Ou, Y-L. and Wang, Z-P., Linear biharmonic maps into Sol, Nil and Heisenberg spaces. Mediterr. J. Math. 5 (2008), 379-394.
  • [17] Perrone, D., Homogeneous contact Riemannian three-manifolds. Illinois J. Math. 42 (1998), 243-256.
  • [18] Troyanov-EPFL, M., L’horizon de SOL. Exposition. Math. 16 (1998).
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Fatma Karaca This is me

Cihan Özgür

Publication Date November 30, 2018
Published in Issue Year 2018 Volume: 11 Issue: 2

Cite

APA Karaca, F., & Özgür, C. (2018). On f-Biharmonic Curves. International Electronic Journal of Geometry, 11(2), 18-27. https://doi.org/10.36890/iejg.545115
AMA Karaca F, Özgür C. On f-Biharmonic Curves. Int. Electron. J. Geom. November 2018;11(2):18-27. doi:10.36890/iejg.545115
Chicago Karaca, Fatma, and Cihan Özgür. “On F-Biharmonic Curves”. International Electronic Journal of Geometry 11, no. 2 (November 2018): 18-27. https://doi.org/10.36890/iejg.545115.
EndNote Karaca F, Özgür C (November 1, 2018) On f-Biharmonic Curves. International Electronic Journal of Geometry 11 2 18–27.
IEEE F. Karaca and C. Özgür, “On f-Biharmonic Curves”, Int. Electron. J. Geom., vol. 11, no. 2, pp. 18–27, 2018, doi: 10.36890/iejg.545115.
ISNAD Karaca, Fatma - Özgür, Cihan. “On F-Biharmonic Curves”. International Electronic Journal of Geometry 11/2 (November 2018), 18-27. https://doi.org/10.36890/iejg.545115.
JAMA Karaca F, Özgür C. On f-Biharmonic Curves. Int. Electron. J. Geom. 2018;11:18–27.
MLA Karaca, Fatma and Cihan Özgür. “On F-Biharmonic Curves”. International Electronic Journal of Geometry, vol. 11, no. 2, 2018, pp. 18-27, doi:10.36890/iejg.545115.
Vancouver Karaca F, Özgür C. On f-Biharmonic Curves. Int. Electron. J. Geom. 2018;11(2):18-27.