Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A metrical approach to Finsler geometry   In the standard approach to Finsler geometry the metric is defined as a
vertical Hessian and the Chern or Cartan connections appear as just two among
many possible natural linear connections on the pullback tangent bundle. Here
it is shown that the Hessian nature of the metric, the non-linear connection
and the Chern or Cartan connections can be derived from a few compatibility
axioms between metric and Finsler connection. This result provides a metric
foundation to Finsler geometry and hence justifies the claim that ``Finsler
geometry is Riemannian geometry without the quadratic restriction''. The paper
also contains a study of the compatibility condition to be placed between the
metric and the non-linear connection.

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The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph