Doubly Warped Product Finsler Manifolds with Some Non-Riemannian Curvature Properties

Details Doubly Warped Product Finsler Manifolds with Some Non-Riemannian Curvature Properties Doubly Warped Product Finsler Manifolds with Some Non-Riemannian Curvature Properties

2011-10-31

arxiv.org/abs/1110.6826v1

Mathematics

Differential Geometry

Scientific paper

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.

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