2011/10/31 by E. Peyghan, Akbar Tayebi, A. Tayebi +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #math.DG
paper · pdf · doi:10.48550/arxiv.1110.6826
arxiv created 2011/10/31 · arxiv updated 2011/11/01
In this paper, we consider doubly warped product (DWP) Finsler manifolds with some non-Riemannian curvature properties. First, we study Berwald and isotropic mean Berwald DWP-Finsler manifolds. Then we prove that every proper Douglas DWP-Finsler manifold is Riemannian. We show that a proper DWP-manifold is Landsbergian if and only it is Berwaldian. In continue, we prove that every relatively isotropic Landsberg DWP-manifold is a Landsberg manifold. We show that a relatively isotropic mean Landsberg warped product manifold is a weakly Landsberg manifold. Finally, we show that there is no any locally dually flat proper DWP-Finsler manifold.