On doubly warped product Finsler manifolds |
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Authors: | Esmaeil Peyghan Akbar Tayebi |
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Institution: | a Department of Mathematics, Faculty of Science, Arak University, Arak, Iranb Faculty of Science, Department of Mathematics, University of Qom, Qom, Iran |
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Abstract: | In this paper, we introduce horizontal and vertical warped product Finsler manifolds. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemannian curvatures of doubly warped product Finsler manifold and its components, and consider the cases that this manifold is flat or has scalar flag curvature. We define the doubly warped Sasaki-Matsumoto metric for warped product manifolds and find a condition under which the horizontal and vertical tangent bundles are totally geodesic. We obtain some conditions under which a foliated manifold reduces to a Reinhart manifold. Finally, we study an almost complex structure on the tangent bundle of a doubly warped product Finsler manifold. |
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Keywords: | Doubly warped product manifold Sasaki-Matsumoto lift metric Vaisman connection Reinhart manifold Kä hler structure |
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