# Finsler metric

From Encyclopedia of Mathematics

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.

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#### 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) |

**How to Cite This Entry:**

Finsler metric.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Finsler_metric&oldid=32097

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article