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arXiv · 1509.09172

A note on 2-dimensional Finsler manifold

Morteza Faghfouri·Rahim Hosseinoghli
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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{\partial g^{ij}}{\partial y^k}\dfrac{\partial f}{\partial x^i}=0, $ a Riemannian manifold? The problem for $n>2$ remains open.

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Morteza Faghfouri, Rahim Hosseinoghli. 2015-09-30. A note on 2-dimensional Finsler manifold. https://doi.org/10.5373/jarpm.2147.092814

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