Displaying similar documents to “Conformal vector fields on tangent bundle of Finsler manifolds.”

On the conformal theory of Ichijyō manifolds

Szakál, Sz.

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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...