Displaying similar documents to “On Berwald and Wagner manifolds.”

On the conformal theory of Ichijyō manifolds

Szakál, Sz.

Similarity:

Some special linear connection introduced in the Finsler space by Ichijyō has the property that the curvature tensors under conformal changes remain invariant. Two Ichijyō manifolds ( M , E , ∇ ) and ( M , E ¯ , ∇ ¯ ) are said to be conformally equivalent if E ¯ = ( exp σ v ) E , σ ∈ C ∞ ( M ) .It is proved, that in this case, the following assertions are equivalent: 1. σ is constant, 2. h ∇ = h ∇ ¯ , 3. S ∇ = S ∇ ¯ , 4. t ∇ = t ∇ ¯ .It is also proved (when the above conditions are satisfied) that1. If ( M , E , ∇ ) is a generalized Berwald manifold, then ( M , E ¯ , ∇ ¯ ) is also a generalized Berwald...

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

Esmaeil Peyghan, Akbar Tayebi, Behzad Najafi (2012)

Annales Polonici Mathematici

Similarity:

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...

Conformal ℱ-harmonic maps for Finsler manifolds

Jintang Li (2014)

Colloquium Mathematicae

Similarity:

By introducing the ℱ-stress energy tensor of maps from an n-dimensional Finsler manifold to a Finsler manifold and assuming that (n-2)ℱ(t)'- 2tℱ(t)'' ≠ 0 for any t ∈ [0,∞), we prove that any conformal strongly ℱ-harmonic map must be homothetic. This assertion generalizes the results by He and Shen for harmonics map and by Ara for the Riemannian case.