Killing vector fields of horizontal Liouville type |
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Authors: | Esmaeil Peyghan Akbar Tayebi |
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Affiliation: | 1. Department of Mathematics, Faculty of Science, University of Arak, Arak, Iran;2. Department of Mathematics, Faculty of Science, Qom University, Qom, Iran |
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Abstract: | On a slit tangent bundle endowed with a Riemannian metric of Sasaki–Finsler type, we introduce two vector fields of horizontal Liouville type and prove that these vector fields are Killing if and only if the base Finsler manifold is of positive constant curvature. In the special case of one of them, we show that if it is Killing vector field then the base manifold is Einstein–Finsler manifold. |
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