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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap105-3-6,
author = {Esmaeil Peyghan and Akbar Tayebi and Behzad Najafi},
title = {Doubly warped product Finsler manifolds with some non-Riemannian curvature properties},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {293-311},
zbl = {1253.53069},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap105-3-6}
}
Esmaeil Peyghan; Akbar Tayebi; Behzad Najafi. Doubly warped product Finsler manifolds with some non-Riemannian curvature properties. Annales Polonici Mathematici, Tome 105 (2012) pp. 293-311. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap105-3-6/