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

Volume 105 / 2012

Esmaeil Peyghan, Akbar Tayebi, Behzad Najafi Annales Polonici Mathematici 105 (2012), 293-311 MSC: Primary 53C60; Secondary 53C25. DOI: 10.4064/ap105-3-6

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.

Authors

  • Esmaeil PeyghanDepartment of Mathematics
    Faculty of Science
    Arak University
    Arak 38156-8-8349, Iran
    e-mail
  • Akbar TayebiDepartment of Mathematics
    Faculty of Science
    University of Qom
    Qom, Iran
    e-mail
  • Behzad NajafiDepartment of Mathematics
    Faculty of Science
    Shahed University
    Tehran, Iran
    e-mail

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