Let be a compact boundaryless Landsberg manifold. In this work, a necessary and sufficient condition for a vector field on to be harmonic is obtained. Next, on a compact boundaryless Finsler manifold of zero flag curvature, a necessary and sufficient condition for a vector field to be harmonic is found. Furthermore, the nonexistence of harmonic vector fields on a compact Landsberg manifold is studied and an upper bound for the first de Rham cohomology group is obtained.
Soit une variété landsbergienne compacte sans bord. Dans cet article, il est obtenu une condition nécessaire et suffisante pour qu'un champ de vecteurs sur soit harmonique. On donne ensuite un énoncé analogue sur une variété finslérienne compacte sans bord. En outre, on étudie la non-existence de champs de vecteurs harmoniques sur les variétés landsbergiennes compactes et, enfin, une borne supérieure pour le premier groupe de cohomologie de de Rham est obtenue.
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Alireza Shahi 1; Behroz Bidabad 1
@article{CRMATH_2014__352_9_737_0, author = {Alireza Shahi and Behroz Bidabad}, title = {Harmonic vector fields on {Landsberg} manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {737--741}, publisher = {Elsevier}, volume = {352}, number = {9}, year = {2014}, doi = {10.1016/j.crma.2014.08.002}, language = {en}, }
Alireza Shahi; Behroz Bidabad. Harmonic vector fields on Landsberg manifolds. Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 737-741. doi : 10.1016/j.crma.2014.08.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.08.002/
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