Explore: Finsler Spaces

geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski norm F(x, −) is provided on each tangent space TxM, that

metric g, then (M, g) is a symmetric Finsler space. The analogue of this theorem for rank-one symmetric spaces has not been proven yet. Another exposition

of Riemann curvature to Finsler spaces, Berwald has been credited as the founder of differential geometry of Finsler spaces. On 22 October 1941, the

the rational numbers. Metric spaces are also studied in their own right in metric geometry and analysis on metric spaces. Many of the basic notions of

functional analysis Finsler manifold, where the length of each tangent vector is determined by a norm Inner product space, normed vector spaces where the norm

the parent space which retains the same structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological

1970. Finsler's thesis work concerned differential geometry, and Finsler spaces were named after him by Élie Cartan in 1934. The Hadwiger–Finsler inequality

underlying Finsler (or Riemannian) manifold are described by this spray for the following reasons: Since gξ is positive definite for Finsler spaces, every

norm defined on each tangent space. Riemannian manifolds are special cases of the more general Finsler manifolds. A Finsler structure on a manifold M {\displaystyle

)\\0&&\end{bmatrix}}.} Busemann, Herbert (1955), "On normal coordinates in Finsler spaces", Mathematische Annalen, 129: 417–423, doi:10.1007/BF01362381, ISSN 0025-5831