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A continuous real function defined on the tangent bundle of an -dimensional smooth manifold is said to be a Finsler metric if
1. is differentiable at ,
2. for any element and any real number ,
3. Denoting the metric
then is a positive definite matrix.
A smooth manifold with a Finsler metric is called a Finsler space.
REFERENCES:
Iyanaga, S. and Kawada, Y. (Eds.). "Finsler Spaces." §161 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 540-542, 1980.
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