A note on 2-dimensional Finsler manifold

2015/09/30 by Morteza Faghfouri, Rahim Hosseinoghli
Mathematics · #math.DG #msc:53C60 #msc:53C25

paper · pdf · doi:10.5373/jarpm.2147.092814

arXiv admin note: text overlap with arXiv:1110.6826 by other authors

arxiv created 2015/09/30 · arxiv updated 2015/12/22

Abstract

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 \dfrac∂ g^ij∂ y^k\dfrac∂ f∂ xⁱ=0, a Riemannian manifold? The problem for n>2 remains open.

Citations

• Doubly Warped Product Finsler Manifolds with Some Non-Riemannian Curvature Properties