Finsler metric

A metric of a space that can be given by a real positive-definite convex function $F(x,y)$ of coordinates of $x$ and components of contravariant vectors $y$ acting at the point $x$. A space supplied with a Finsler metric is called a Finsler space, and its geometry Finsler geometry.

References

[a1]	H. Busemann, "The geometry of geodesics" , Acad. Press (1955)
[a2]	W. Rinow, "Die innere Geometrie der metrischen Räume" , Springer (1961)
[a3]	H. Rund, "The differential geometry of Finsler spaces" , Springer (1959)