Difference between revisions of "Finsler metric"
From Encyclopedia of Mathematics
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| − | A metric of a space that can be given by a real positive-definite convex function | + | {{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]]. | |
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====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=15174
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