A note on 2-dimensional Finsler manifold

الأصل · EN

We solve the following problem for n=2: Is any n-dimensional Finsler manifold (M, F) with a function f which is nonconstant and smooth on M satisfying ∂ gij∂ yᵏ∂ f/∂ xⁱ=0, a Riemannian manifold? The problem for n>2 remains open.