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.