Harmonic vector fields on Landsberg manifolds |
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Authors: | Alireza Shahi Behroz Bidabad |
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Affiliation: | Faculty of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, 15914 Tehran, Iran |
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Abstract: | Let (M,F) be a compact boundaryless Landsberg manifold. In this work, a necessary and sufficient condition for a vector field on (M,F) 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. |
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