# Finsler Geometry

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## Finsler geometry

[′fin·slər jē′äm·ə·trē] (mathematics)

The study of the geometry of a manifold in terms of the various possible metrics on it by means of Finsler structures.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Finsler Geometry

the theory of Finsler spaces, in which the differential *ds* of the arc length of a curve depends on the point under consideration in the space and on the choice of direction at the point. In other words, Finsler geometry is a theory of spaces where lengths are measured in small steps and the scale of measurement depends on the point of the space and the choice of direction at the point. The concept of such spaces was first introduced by B. Riemann in 1854. The first detailed examination of the theory of the spaces was presented by the German mathematician P. Finsler in 1918. Finsler geometry is widely used in the calculus of variations and in theoretical physics.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.