Doubly warped product Finsler manifolds with some non-Riemannian curvature properties
Tom 105 / 2012
Annales Polonici Mathematici 105 (2012), 293-311 MSC: Primary 53C60; Secondary 53C25. DOI: 10.4064/ap105-3-6
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 if it is Berwaldian. Then 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 locally dually flat proper DWP-Finsler manifold.