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Difference between revisions of "Finsler metric"

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A metric of a space that can be given by a real positive-definite convex function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f040/f040400/f0404001.png" /> of coordinates of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f040/f040400/f0404002.png" /> and components of contravariant vectors <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f040/f040400/f0404003.png" /> acting at the point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f040/f040400/f0404004.png" />. A space supplied with a Finsler metric is called a Finsler space, and its geometry [[Finsler geometry|Finsler geometry]].
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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|Finsler geometry]].
  
  

Revision as of 16:24, 1 May 2014

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.


Comments

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://encyclopediaofmath.org/index.php?title=Finsler_metric&oldid=15174
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article