Doubly warped product Finsler manifolds with some non-Riemannian curvature properties

Esmaeil Peyghan, Akbar Tayebi, and Behzad Najafi. "Doubly warped product Finsler manifolds with some non-Riemannian curvature properties." Annales Polonici Mathematici 105.3 (2012): 293-311. <http://eudml.org/doc/280261>.

@article{EsmaeilPeyghan2012,
abstract = {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.},
author = {Esmaeil Peyghan, Akbar Tayebi, Behzad Najafi},
journal = {Annales Polonici Mathematici},
keywords = {doubly warped product manifold; non-Riemannian curvatures},
language = {eng},
number = {3},
pages = {293-311},
title = {Doubly warped product Finsler manifolds with some non-Riemannian curvature properties},
url = {http://eudml.org/doc/280261},
volume = {105},
year = {2012},
}

TY - JOUR
AU - Esmaeil Peyghan
AU - Akbar Tayebi
AU - Behzad Najafi
TI - Doubly warped product Finsler manifolds with some non-Riemannian curvature properties
JO - Annales Polonici Mathematici
PY - 2012
VL - 105
IS - 3
SP - 293
EP - 311
AB - 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.
LA - eng
KW - doubly warped product manifold; non-Riemannian curvatures
UR - http://eudml.org/doc/280261
ER -