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ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS

Year 2012, Volume: 5 Issue: 1, 90 - 100, 30.04.2012

M. Djaa A. M. Cherıf K. Zegga S. Ouakkas

Abstract

 

Keywords

Harmonic maps bi-harmonic maps f-harmonic maps f-biharmonic maps

References

  • [1] Ara, M., Geometry of F -Harmonic maps; Kodai Math. J. 22, 243-263, (1999).
  • [2] Baird, P. and Wood, J.C., Harmonic morphisms between Riemannain manifolds. Clarendon Press Oxford 2003.
  • [3] Baird, P and Gudmundson, S., p-harmoinc maps and minimal submanifolds, Math. Ann. 294 (1992), 611-624.
  • [4] Baird, P., Fardoun, A. and S. Ouakkas, Conformal and semi-conformal biharmonic maps,Annals of global analysis and geometry, 34 (2008),403–414.
  • [5] Course, .N, f-harmonic maps which map the boundary of the domain to one point in the target; New York Journal of Mathematics. 13, (2007), 423-435.
  • [6] Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds, Amer. J. Maths, 86(1964).
  • [7] Eells, J. and Lemaire, L., Another report on harmonic maps, Bull. London Math. Soc. 20 (1988), 385-524.
  • [8] Jiang, G.Y.: Harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser. A. 7, 389-402 (1986).
  • [9] Loubeau, E. and Ou, Y.L., The caracterization of biharmonic morphisms; Differential geometry and its applications (Opava 2001) Math. Publ. 3(2001), 31-41.
  • [10] Ouakkas, S., Nasri, R. and Djaa, M., On the f-harmonic and f-biharmonic maps, JP Journal of Geometry and Topology, Volume 10, Number 1, 2010, Pages 11-27 Mars 2010.
  • [11] Ouakkas, S., Biharmonic maps, conformal deformations and the Hopf maps, Differential Geometry and its Applications,26 (2008), 495–502.
  • [12] Oniciuc, C., Biharmonic maps between Riemannian manifolds, An.Stinj. Univ Al.I. Cusa Iasi Mat. 48, (2002), 237-248.

Year 2012, Volume: 5 Issue: 1, 90 - 100, 30.04.2012

M. Djaa A. M. Cherıf K. Zegga S. Ouakkas

Abstract

References

  • [1] Ara, M., Geometry of F -Harmonic maps; Kodai Math. J. 22, 243-263, (1999).
  • [2] Baird, P. and Wood, J.C., Harmonic morphisms between Riemannain manifolds. Clarendon Press Oxford 2003.
  • [3] Baird, P and Gudmundson, S., p-harmoinc maps and minimal submanifolds, Math. Ann. 294 (1992), 611-624.
  • [4] Baird, P., Fardoun, A. and S. Ouakkas, Conformal and semi-conformal biharmonic maps,Annals of global analysis and geometry, 34 (2008),403–414.
  • [5] Course, .N, f-harmonic maps which map the boundary of the domain to one point in the target; New York Journal of Mathematics. 13, (2007), 423-435.
  • [6] Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds, Amer. J. Maths, 86(1964).
  • [7] Eells, J. and Lemaire, L., Another report on harmonic maps, Bull. London Math. Soc. 20 (1988), 385-524.
  • [8] Jiang, G.Y.: Harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser. A. 7, 389-402 (1986).
  • [9] Loubeau, E. and Ou, Y.L., The caracterization of biharmonic morphisms; Differential geometry and its applications (Opava 2001) Math. Publ. 3(2001), 31-41.
  • [10] Ouakkas, S., Nasri, R. and Djaa, M., On the f-harmonic and f-biharmonic maps, JP Journal of Geometry and Topology, Volume 10, Number 1, 2010, Pages 11-27 Mars 2010.
  • [11] Ouakkas, S., Biharmonic maps, conformal deformations and the Hopf maps, Differential Geometry and its Applications,26 (2008), 495–502.
  • [12] Oniciuc, C., Biharmonic maps between Riemannian manifolds, An.Stinj. Univ Al.I. Cusa Iasi Mat. 48, (2002), 237-248.
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

M. Djaa This is me

A. M. Cherıf This is me

K. Zegga This is me

S. Ouakkas This is me

Publication Date April 30, 2012
Published in Issue Year 2012 Volume: 5 Issue: 1

Cite

APA Djaa, M., Cherıf, A. M., Zegga, K., Ouakkas, S. (2012). ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS. International Electronic Journal of Geometry, 5(1), 90-100.
AMA Djaa M, Cherıf AM, Zegga K, Ouakkas S. ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS. Int. Electron. J. Geom. April 2012;5(1):90-100.
Chicago Djaa, M., A. M. Cherıf, K. Zegga, and S. Ouakkas. “ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS”. International Electronic Journal of Geometry 5, no. 1 (April 2012): 90-100.
EndNote Djaa M, Cherıf AM, Zegga K, Ouakkas S (April 1, 2012) ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS. International Electronic Journal of Geometry 5 1 90–100.
IEEE M. Djaa, A. M. Cherıf, K. Zegga, and S. Ouakkas, “ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS”, Int. Electron. J. Geom., vol. 5, no. 1, pp. 90–100, 2012.
ISNAD Djaa, M. et al. “ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS”. International Electronic Journal of Geometry 5/1 (April 2012), 90-100.
JAMA Djaa M, Cherıf AM, Zegga K, Ouakkas S. ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS. Int. Electron. J. Geom. 2012;5:90–100.
MLA Djaa, M. et al. “ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS”. International Electronic Journal of Geometry, vol. 5, no. 1, 2012, pp. 90-100.
Vancouver Djaa M, Cherıf AM, Zegga K, Ouakkas S. ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS. Int. Electron. J. Geom. 2012;5(1):90-100.