Geodesic
Doubly warped product Finsler manifolds with some non-Riemannian curvature properties
Esmaeil Peyghan1 ; Akbar Tayebi2 ; Behzad Najafi3
1Department of Mathematics Faculty of Science Arak University Arak 38156-8-8349, Iran
2Department of Mathematics Faculty of Science University of Qom Qom, Iran
3Department of Mathematics Faculty of Science Shahed University Tehran, Iran
Annales Polonici Mathematici, Tome 105 (2012) no. 3, pp. 293-311
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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.
DOI : 10.4064/ap105-3-6
Keywords: consider doubly warped product dwp finsler manifolds non riemannian curvature properties first study berwald isotropic mean berwald dwp finsler manifolds prove every proper douglas dwp finsler manifold riemannian proper dwp manifold landsbergian only berwaldian prove every relatively isotropic landsberg dwp manifold landsberg manifold relatively isotropic mean landsberg warped product manifold weakly landsberg manifold finally there locally dually flat proper dwp finsler manifold

Esmaeil Peyghan  1   ; Akbar Tayebi  2   ; Behzad Najafi  3

1 Department of Mathematics Faculty of Science Arak University Arak 38156-8-8349, Iran
2 Department of Mathematics Faculty of Science University of Qom Qom, Iran
3 Department of Mathematics Faculty of Science Shahed University Tehran, Iran 
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     title = {Doubly warped product {Finsler} manifolds
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     journal = {Annales Polonici Mathematici},
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Esmaeil Peyghan; Akbar Tayebi; Behzad Najafi. Doubly warped product Finsler manifolds
 with some non-Riemannian curvature properties. Annales Polonici Mathematici, Tome 105 (2012) no. 3, pp. 293-311. doi: 10.4064/ap105-3-6

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