## Finsler Metric

A continuous real function defined on the Tangent Bundle of an -D Differentiable 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 Differentiable Manifold with a Finsler metric is called a Finsler Space.

Iyanaga, S. and Kawada, Y. (Eds.). Finsler Spaces.'' §161 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 540-542, 1980.