Finsler metric

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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.


[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)
How to Cite This Entry:
Finsler metric. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article