Annales Mathématiques
Blaise Pascal
no. 2
Some examples of harmonic maps for g-natural metrics
Mohamed Tahar Kadaoui Abbassi1 ; Giovanni Calvaruso2 ; Domenico Perrone2
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, Tome 16 (2009) no. 2, pp. 305-320.

On produit des nouveaux exemples d’applications harmoniques, ayant chacune comme espace de départ une variété (M,g) á courbure constante et comme espace d’arrivée son fibré tangent TM, muni d’une métrique g-naturelle Riemannienne appropriée. En particulier, on va déterminer une famille de métriques g-naturelles Riemanniennes G sur T𝕊 2 , par rapport auxquelles tous les champs de vecteurs gradients conformes définissent des applications harmoniques de 𝕊 2 dans (T𝕊 2 ,G).

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 T𝕊 2 , with respect to which all conformal gradient vector fields define harmonic maps from 𝕊 2 into (T𝕊 2 ,G).

DOI : 10.5802/ambp.269
Classification : 58E20, 53C43
Mots clés : harmonic map, tangent bundle, vector fields, $g$-natural metrics, spaces of constant curvature.

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. 
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Mohamed Tahar Kadaoui Abbassi; Giovanni Calvaruso; Domenico Perrone. Some examples of harmonic maps for $g$-natural metrics. Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 2, pp. 305-320. doi : 10.5802/ambp.269. https://ambp.centre-mersenne.org/articles/10.5802/ambp.269/

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