Abstract
We regard special Finsler manifolds which are almost Riemannian. These Finsler metrics allow to construct globally an osculating Riemannian metric with a LEVI-CIVITA connection that can be well described by Finslerian invariants. An application of this concept will be given in a paper about the “pinching problem”, which will be published soon. For locally almost euclidian metrics we proof generalisations of the comparison theorem of RAUCH and the theorem of SHIKATA.
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