mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski norm F(x,...

inner product. Any Riemannian manifold is a Finsler manifold. Lie groups, named after Sophus Lie, are differentiable manifolds that carry also the structure...

Generalizations of Riemannian manifolds include pseudo-Riemannian manifolds, Finsler manifolds, and sub-Riemannian manifolds. In 1827, Carl Friedrich Gauss...

Topological manifold Almost complex manifold Almost symplectic manifold Calibrated manifold Complex manifold Contact manifold CR manifold Finsler manifold Hermitian...

smooth manifold can be given a non-Riemannian pseudo-Riemannian structure; there are topological restrictions on doing so. A Finsler manifold is a different...

Holmes–Thompson volume of a measurable set A {\displaystyle A} in a Finsler manifold ( M , F ) {\displaystyle (M,F)} can be defined as Vol HT ⁡ ( A ) :=...

length in Minkowski space The norm defined in the tangent bundle of a Finsler manifold The vector p-norm The norm defined by a Minkowski functional This disambiguation...

non-linear connection arising in this manner is that associated to a Finsler manifold. Equation (1) is invariant under affine reparameterizations; that is...

structure in differential geometry Rizza manifold – almost complex manifold equipped with a compatible Finsler structurePages displaying wikidata descriptions...

Lorentzian manifold, which is the mathematical basis of Einstein's general relativity theory of gravity. Finsler geometry has Finsler manifolds as the main...

sphere bundle can easily accommodate Finsler manifolds as well. Specifically, if M is a manifold equipped with a Finsler metric F : TM → R, then the unit...

Rizza manifold, named after Giovanni Battista Rizza, is an almost complex manifold also supporting a Finsler structure: this kind of manifold is also...

Riemannian or Pseudo-Riemannian manifold. By contrast, in general there is no way to define normal coordinates for Finsler manifolds in a way that the exponential...

by the norm Banach–Mazur compactum – Concept in functional analysis Finsler manifold, where the length of each tangent vector is determined by a norm Inner...

Paul Finsler (born 11 April 1894, in Heilbronn, Germany, died 29 April 1970 in Zurich, Switzerland) was a German and Swiss mathematician. Finsler did his...

induced on the corresponding bundle (e.g., the geodesic spray on Finsler manifolds.) Since the early 1980s, jet bundles have appeared as a concise way...

This follows from Ivanov's theorem since the Hausdorff area of a Finsler manifold is never less than the Holmes–Thompson area, and the two areas are...

fallback Differentiation in Fréchet spaces Finsler manifold – Generalization of Riemannian manifolds Fréchet manifold – topological space modeled on a Fréchet...

Banach manifold – Manifold modeled on Banach spaces Differentiation in Fréchet spaces Finsler manifold – Generalization of Riemannian manifolds Fréchet...

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

Riemannian manifold Pseudo-Riemannian manifold Basic introduction to the mathematics of curved spacetime Clifford algebra Finsler manifold List of coordinate...

(mathematics) Secondary vector bundle structure Finsler manifold J.M.Lee, Introduction to Smooth Manifolds, Springer-Verlag, 2003. P.Michor. Topics in Differential...

Riemannian manifold. Suppose that C 2 {\displaystyle C^{2}} Finsler metric on M with the same geodesics as in the metric g is given. Then the Finsler metric...

curves.) Analogously, other manifolds in which a length is defined included Finsler manifolds and sub-Riemannian manifolds. Any complete and convex metric...

universe. Finsler geometry a branch of differential geometry whose main object of study is Finsler manifolds, a generalisation of a Riemannian manifolds. First...

displaying short descriptions of redirect targets Finsler manifold – Generalization of Riemannian manifolds Hadwiger's theorem – Theorem in integral geometry...

Differential Geometry Riemannian and Finsler Manifolds Symplectic Geometry Global Analysis, Analysis on Manifolds Geometric Theory of Differential Equations...

Intrinsic metric Pseudo-Riemannian manifold Sub-Riemannian manifold Finsler geometry General relativity G2 manifold Information geometry Fisher information...

branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent...

asymmetric seminorm on X . {\displaystyle X.} Finsler manifold – Generalization of Riemannian manifolds Minkowski functional – Function made from a set...