Some examples of harmonic maps for g -natural metrics

Mohamed Tahar Kadaoui Abbassi[1]; Giovanni Calvaruso[2]; Domenico Perrone[2]

  • [1] Département des Mathématiques, Faculté des sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdallah, B.P. 1796, Fès-Atlas, Fès, Morocco
  • [2] Dipartimento di Matematica “E. De Giorgi”, Università del Salento, 73100 Lecce, ITALY.

Annales mathématiques Blaise Pascal (2009)

  • Volume: 16, Issue: 2, page 305-320
  • ISSN: 1259-1734

Abstract

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We produce new examples of harmonic maps, having as source manifold a space ( M , g ) of constant curvature and as target manifold its tangent bundle T M , equipped with a suitable Riemannian g -natural metric. In particular, we determine a family of Riemannian g -natural metrics G on T 𝕊 2 , with respect to which all conformal gradient vector fields define harmonic maps from 𝕊 2 into ( T 𝕊 2 , G ) .

How to cite

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Abbassi, Mohamed Tahar Kadaoui, Calvaruso, Giovanni, and Perrone, Domenico. "Some examples of harmonic maps for $g$-natural metrics." Annales mathématiques Blaise Pascal 16.2 (2009): 305-320. <http://eudml.org/doc/10582>.

@article{Abbassi2009,
abstract = {We produce new examples of harmonic maps, having as source manifold a space $(M,g)$ of constant curvature and as target manifold its tangent bundle $TM$, equipped with a suitable Riemannian $g$-natural metric. In particular, we determine a family of Riemannian $g$-natural metrics $G$ on $T\mathbb\{S\}^2$, with respect to which all conformal gradient vector fields define harmonic maps from $\mathbb\{S\}^2$ into $(T\mathbb\{S\}^2,G)$.},
affiliation = {Département des Mathématiques, Faculté des sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdallah, B.P. 1796, Fès-Atlas, Fès, Morocco; Dipartimento di Matematica “E. De Giorgi”, Università del Salento, 73100 Lecce, ITALY.; Dipartimento di Matematica “E. De Giorgi”, Università del Salento, 73100 Lecce, ITALY.},
author = {Abbassi, Mohamed Tahar Kadaoui, Calvaruso, Giovanni, Perrone, Domenico},
journal = {Annales mathématiques Blaise Pascal},
keywords = {harmonic map; tangent bundle; vector fields; $g$-natural metrics; spaces of constant curvature; tangent bundle, vector fields; -natural metrics},
language = {eng},
month = {7},
number = {2},
pages = {305-320},
publisher = {Annales mathématiques Blaise Pascal},
title = {Some examples of harmonic maps for $g$-natural metrics},
url = {http://eudml.org/doc/10582},
volume = {16},
year = {2009},
}

TY - JOUR
AU - Abbassi, Mohamed Tahar Kadaoui
AU - Calvaruso, Giovanni
AU - Perrone, Domenico
TI - Some examples of harmonic maps for $g$-natural metrics
JO - Annales mathématiques Blaise Pascal
DA - 2009/7//
PB - Annales mathématiques Blaise Pascal
VL - 16
IS - 2
SP - 305
EP - 320
AB - We produce new examples of harmonic maps, having as source manifold a space $(M,g)$ of constant curvature and as target manifold its tangent bundle $TM$, equipped with a suitable Riemannian $g$-natural metric. In particular, we determine a family of Riemannian $g$-natural metrics $G$ on $T\mathbb{S}^2$, with respect to which all conformal gradient vector fields define harmonic maps from $\mathbb{S}^2$ into $(T\mathbb{S}^2,G)$.
LA - eng
KW - harmonic map; tangent bundle; vector fields; $g$-natural metrics; spaces of constant curvature; tangent bundle, vector fields; -natural metrics
UR - http://eudml.org/doc/10582
ER -

References

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  1. M. T. K. Abbassi, G. Calvaruso, D. Perrone, Harmonic sections of tangent bundles equipped with Riemannian g -natural metrics, (2007) Zbl1226.53062
  2. Mohamed Tahar Kadaoui Abbassi, Maâti Sarih, On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. (Brno) 41 (2005), 71-92 Zbl1114.53015MR2142144
  3. Mohamed Tahar Kadaoui Abbassi, Maâti Sarih, On some hereditary properties of Riemannian g -natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl. 22 (2005), 19-47 Zbl1068.53016MR2106375
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  11. Odette Nouhaud, Applications harmoniques d’une variété riemannienne dans son fibré tangent. Généralisation, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), A815-A818 Zbl0349.53015MR431035
  12. C. Oniciuc, The tangent bundles and harmonicity, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 43 (1997), 151-172 (1998) Zbl0989.53039MR1679113
  13. J. H. Sampson, Some properties and applications of harmonic mappings, Ann. Sci. École Norm. Sup. (4) 11 (1978), 211-228 Zbl0392.31009MR510549
  14. Aristide Sanini, Maps between Riemannian manifolds with critical energy with respect to deformations of metrics, Rend. Mat. (7) 3 (1983), 53-63 Zbl0514.53037MR710809
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  16. Y. L. Xin, Some results on stable harmonic maps, Duke Math. J. 47 (1980), 609-613 Zbl0513.58019MR587168

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