Namespaces
Variants
Actions

Difference between revisions of "Finsler metric"

From Encyclopedia of Mathematics
Jump to: navigation, search
(TeX)
m (details)
 
Line 1: Line 1:
 
{{TEX|done}}
 
{{TEX|done}}
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]].
+
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====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  H. Busemann,  "The geometry of geodesics" , Acad. Press  (1955)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  W. Rinow,  "Die innere Geometrie der metrischen Räume" , Springer  (1961)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  H. Rund,  "The differential geometry of Finsler spaces" , Springer  (1959)</TD></TR></table>
+
<table>
 +
<TR><TD valign="top">[a1]</TD> <TD valign="top">  H. Busemann,  "The geometry of geodesics" , Acad. Press  (1955)</TD></TR>
 +
<TR><TD valign="top">[a2]</TD> <TD valign="top">  W. Rinow,  "Die innere Geometrie der metrischen Räume" , Springer  (1961)</TD></TR>
 +
<TR><TD valign="top">[a3]</TD> <TD valign="top">  H. Rund,  "The differential geometry of Finsler spaces" , Springer  (1959)</TD></TR>
 +
</table>

Latest revision as of 14:53, 8 April 2023

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)
How to Cite This Entry:
Finsler metric. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Finsler_metric&oldid=53680
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article