We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we …
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48 results for “weak Finsler metrics”
The paper finds the Finsler structure of Apollonian weak metric on unit disc.
problem Understanding the Finsler structure of Apollonian weak metric on the unit disc.
method Analyzing the deformation of hyperbolic Poincaré metric by a closed 1-form.
result The Apollonian weak-Finsler structure has bounded below -curvature and flag curvature satisfying .
The paper describes geometric properties of Teichmüller space metrics.
problem Analyzing the geometry of Teichmüller space with weak Finsler metrics.
method Geometric description of unit spheres in weak Finsler metrics.
result Introduced a family of weak Finsler metrics interpolating between Thurston's metric and Teichmüller metric.
David Hilbert discovered in 1895 an important metric that is canonically associated to any convex domain in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof assumes a certain degree of smoothness of the boundary of and refers to a theorem by Busemann and Mayer that…
I do not agree with the authors of papers arXiv:0806.2184 and arXiv:0901.1023v1 (published in Phys. Lett., respectively, B668 (2008) 453 and B676 (2009) 173). They consider that \textit{"In Finsler manifold, there exists a unique linear connection - the Chern connection ... It is torsion freeness and metric compatibili…
In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete Finsler manifold is determined by the normed algebra of all real-valued, bounded and smooth functions with bounded derivative defined on . As a consequence, we obtain: (i) the Finsler structu…
We provide lower bounds on the number of periodic Finsler billiard trajectories inside a quadratically convex smooth closed hypersurface in a -dimensional Finsler space with possibly irreversible Finsler metric. An example of such a system is a billiard in a sufficiently weak magnetic field. The -periodic Fin…
This paper classifies geodesics of projectively flat sprays and introduces a method to determine sprays based on geodesics.
problem Classifying geodesics of projectively flat sprays and determining sprays based on geodesics.
method Introduction of a geodesic method to determine an n-dimensional spray based on a family of curves with 2(n-1) free parameters as geodesics.
result Classification of geodesics of projectively flat sprays and determination of sprays based on geodesics.
In this short note, we prove that if is a weak upper semicontinuous admissible Finsler structure on a domain in , , then the intrinsic distance and differential structures coincide.
Characterizes complex Finsler metrics and their properties.
problem Characterize complex Finsler metrics and their geometric properties.
method Defined the canonical connection and investigated holomorphic sectional curvature tensors and Ricci curvatures.
result Characterizes balanced complex Finsler metrics and provides sufficient and necessary conditions.
The paper extends Sobolev spaces to Finsler manifolds and shows density of smooth functions.
problem Defining and analyzing Sobolev spaces on Finsler manifolds.
method Defining Sobolev spaces for Finsler structures and proving density of smooth functions.
result Smooth functions can approximate weak solutions and functions in Sobolev spaces on Finsler manifolds.
Study on special Finsler metrics with conditions for Riemannian and isotropic properties.
problem Characterizing Finsler metrics with specific geometric properties.
method Analyzing conditions for Riemannian and isotropic properties of AR-Finsler metrics.
result Conditions for isotropic -curvature and mean Landsberg curvature leading to vanishing curvature.
Most Finsler metrics have infinite-dimensional holonomy groups.
problem Understanding the holonomy groups of Finsler metrics.
method Analyzing the set of Finsler metrics on a manifold.
result An open dense subset of Finsler metrics have infinite-dimensional holonomy groups.
Paper studies Landsberg curvature of a specific Finsler metric.
problem Analyzing Landsberg curvature of a particular Finsler metric.
method Derived Landsberg curvature and mean Landsberg curvature of the twisted product Finsler metric.
result Necessary and sufficient conditions for the metric to be Landsberg or weakly Landsberg are established.
New Finsler metrics constructed from -metrics.
problem Exploring new Finsler metrics within the -metric class.
method Constructing new sub-classes of -metrics.
result Presented illustrative examples of new Finsler metrics.
New calculus on spacetimes for nonlinear differential equations.
problem Nonlinear differential equations on metric measure spacetimes.
method Introduces maximal weak subslope and variational calculus.
result Establishes a comparison theorem for nonlinear -d'Alembertian.
Investigate AR-Finsler metrics for local dual flatness and projective flatness.
problem Locally dually and projectively flat AR-Finsler metrics
method Derive necessary and sufficient conditions and a compatibility relation.
result Establish a rigidity result for AR-Finsler metrics.
Study Ricci curvature of homogeneous Finsler spaces with specific metrics.
problem Curvature properties of homogeneous Finsler spaces with -metrics.
method Derived explicit formulae for Ricci curvature and found conditions for vanishing -curvature.
result Spaces with vanishing -curvature and negative Ricci curvature are Riemannian.
New definition of naturally reductive Finsler manifolds using geodesic graphs.
problem Defining naturally reductive Finsler manifolds using geodesic graphs.
method Proposed a new geometrical definition using geodesic graphs and constructed examples of Finsler metrics.
result Explicit examples of Finsler naturally reductive metrics constructed.
New approach connects Finsler geometry's metric and connections.
problem Deriving Finsler geometry's metric and connections from compatibility axioms.
method Compatibility axioms between metric and Finsler connection.
result Metrical formulation of Finsler geometry for field theory.
The paper examines properties of spherical Finsler metrics, proving their semi-C-reducibility and conditions for vanishing mean stretch curvature.
problem Analyzing curvature properties of spherical Finsler metrics.
method Proving semi-C-reducibility and finding conditions for vanishing mean stretch curvature.
result Conditions for a general spherically symmetric Finsler metric to have vanishing mean stretch curvature.
Study cylindrical symmetric Finsler metrics with vanishing Douglas curvature.
problem Understanding Finsler metrics with specific curvature properties.
method Analyzing cylindrically symmetric Finsler metrics and solving differential equations.
result Differential equations for cylindrically symmetric Finsler metrics with vanishing Douglas curvature.
This paper explores new Finsler metrics and their connections to generalized Sakaguchi's Theorem.
problem Understanding the properties of Finsler metrics and their projective invariants.
method Developed and examined weakly-Weyl and generalized weakly-Weyl Finsler metrics.
result Equivalence of weakly-Weyl and -quadratic spherically symmetric Finsler metrics.
Study flag curvature in homogeneous Finsler spaces with a specific metric.
problem Analyzing flag curvature in homogeneous Finsler spaces with a generalized -Kropina metric.
method Provided explicit formula for flag curvature, showed equivalence of definitions, and studied curvature of naturally reductive spaces.
result Equivalence of two definitions of naturally reductive homogeneous Finsler spaces for the generalized -Kropina metric.
The paper examines Finsler metrics under Ricci flow and finds they are Einstein.
problem Understanding Finsler metrics under Ricci flow.
method Investigated C3-like Finsler metrics and proved they are Einstein.
result C3-like Finsler metrics are Einstein under Ricci flow.
Constructs a convex Finsler metric on vector bundles under specific conditions.
problem Creating a convex Finsler metric on vector bundles with positive curvature.
method Uses the negativity of direct image bundles and Minkowski inequality for norms.
result Shows how to upgrade a Kobayashi positive Finsler metric to a convex one.
Study curvature of complex Finsler metrics on Lie groups.
problem Explicitly calculate and characterize curvature of complex Finsler metrics.
method Analyzes left-invariant complex Finsler metrics on Lie groups using their Lie algebra.
result Characterizes conditions for a Finsler metric to be Kähler or weakly Kähler.
New Finsler metrics derived from pedal curves.
problem Constructing new Finsler metrics.
method Using pedal curves or surfaces of other curves/surfaces.
result Generalization of slope metric.
For a standard Finsler metric F on a manifold M, its domain is the whole tangent bundle TM and its fundamental tensor g is positive-definite. However, in many cases (for example, the well-known Kropina and Matsumoto metrics), these two conditions are relaxed, obtaining then either a pseudo-Finsler metric (with arbitrar…
Study Finsler metrics with vanishing Landsberg curvature.
problem Characterize Finsler metrics with specific curvature properties.
method Derive expressions for curvatures, solve PDEs, construct examples.
result Construct non-regular Landsberg metrics not of Berwald type.
The paper explores families of Finsler metrics and their properties.
problem Understanding symmetrizations and combinations of Finsler metrics.
method Introducing two families of metrics derived from a general Finsler metric.
result Characterization of geodesics, completeness, and Finsler properties of the introduced metrics.
Investigates hypersurfaces in Finsler spaces with generalized square metrics.
problem Classifying and understanding hypersurfaces in Finsler spaces with generalized square metrics.
method Examined the generalized square metric F(x,y) = (α(x,y) + β(x,y))^(n+1)/(α^n(x,y)) and its application to Finslerian hypersurfaces.
result Established the classification and existence of first, second, and third kind of hyperplanes in the Finsler manifold.
Study cylindrical symmetric Finsler metrics that are projectively flat.
problem Characterize Finsler metrics that are projectively flat.
method Solve the system of differential equations for cylindrical symmetric Finsler metrics.
result Provide a family of solutions for the projectively flat Finsler metrics.
Study characterizes Finsler metrics with first integrals using specific curvature tensors.
problem Characterizing Finsler metrics with first integrals.
method Used -curvature and mean Berwald curvature to characterize the metrics.
result Characterized a class of Finsler metrics admitting first integrals.
New method approximates anisotropic curve shortening flow.
problem Approximating anisotropic curve shortening flow.
method Weak formulation and finite element approximation.
result Optimal -error bound for approximation.
Paper shows isotropic - and -curvatures are equivalent in warped Finsler metrics.
problem Equivalence of non-Riemannian curvatures in warped product Finsler metrics.
method Study of warped product Finsler metrics.
result Isotropic - and -curvatures are equivalent for these metrics.
On Special Berwald Metricsmath.DG
In this paper, we study a class of Finsler metrics which contains the class of Berwald metrics as a special case. We prove that every Finsler metric in this class is a generalized Douglas-Weyl metric. Then we study isotropic flag curvature Finsler metrics in this class. Finally we show that on this class of Finsler met…
The present paper deals with the Killing correspondence between some Finsler spaces. We consider a Finsler space equipped with a -change of metric and study the Killing correspondence between the original Finsler space and the Finsler space equipped with -change of metric. We obtain necessary and sufficient condi…
In every conformal class of Finsler (or Riemannian) metrics on a closed manifold there exists a residual subset of Finsler metrics, such that, with respect to the residual Finsler metrics, in any non-trivial homotopy class of free loops there is precisely one shortest geodesic loop.
Any Riemannian manifold has a canonical collection of valuations (finitely additive measures) attached to it, known as the intrinsic volumes or Lipschitz-Killing valuations. They date back to the remarkable discovery of H. Weyl that the coefficients of the tube volume polynomial are intrinsic invariants of the metric. …
Study spherically symmetric Finsler metrics with specific curvature properties.
problem Characterize Finsler metrics with scalar and constant flag curvature.
method Analyze spherically symmetric metrics on symmetric spaces with given curvature properties.
result Provide families of Finsler metrics with scalar and constant flag curvature.
Study on geodesics of Finsler metrics derived from Riemannian metrics.
problem Investigating geodesics in Finsler metrics derived from Riemannian metrics.
method Proved geodesic lemma for a family of Riemannian geodesic orbit metrics, analyzed geodesic graphs.
result Derived Finsler metrics have geodesic orbit property and belong to a new class of metrics.
Characterizes spherical Finsler metrics satisfying a specific condition.
problem Spherically symmetric Finsler metrics satisfying the -condition.
method Complete characterization and subclass investigation within Landsberg category.
result Identifies precise conditions for metrics satisfying the -condition.
The class of spherically symmetric Finsler metrics is studied and locally dually flat and projectively flat spherically symmetric Finsler metrics is classified.
New Finsler flow on 2-torus has chaotic dynamics.
problem Constructing chaotic dynamics on a 2-torus.
method Using Berger and Turaev's theorem, constructing a Finsler metric.
result Found a Finsler geodesic flow with positive metric entropy.
In this paper, we give the general form of spherically symmetric Finsler metrics in and surprisedly find that many well-known Finsler metrics belong to this class. Then we explicitly express projective metrics of this type. The necessary and sufficient conditions that projective Finsler metrics with spherical sym…
Paper solves open problem in complex Finsler geometry.
problem Existence of non-Kähler weakly Kähler Finsler metrics.
method Constructs a family of weakly Kähler Finsler metrics.
result Proves uniformization theorem for unitary invariant complex Randers metrics.
A Riemannian metric is of constant curvature if and only if it is locally projectively flat. There are infinitely many locally projectively flat Finsler metrics of constant curvature, that are special solutions to the Hilbert's Fourth Problem. In this paper, we use the technique in the paper titled "Finsler metrics wit…