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...

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

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

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

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

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...

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...

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...

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 ) :=...

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

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...

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

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

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...

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

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

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

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

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...

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

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...

generalizes to any Riemannian surface or more generally to two-dimensional Finsler manifolds; the integral is then performed with the natural measure on the space...

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

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

may study differentiable manifolds equipped with a connection, a metric (which may be Riemannian, pseudo-Riemannian, or Finsler), a special sort of distribution...

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

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

connection Einstein manifold Euclidean geometry Exponential map Exponential map (Lie theory), Exponential map (Riemannian geometry) Finsler metric A generalization...