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 metric structures”
The study explores new metric structures on manifolds, linking them to Einstein metrics.
problem Characterizing and understanding weak K-contact manifolds and their properties.
method Analyzing weak K-contact manifolds and their properties, including the parallel Ricci tensor and generalized Ricci soliton structures.
result Sufficient conditions for weak K-contact manifolds with specific properties to be Einstein manifolds.
New structure with B-metric extends classical almost contact structures.
problem Extending classical almost contact structures with new geometric properties.
method Introduced and studied weak almost contact structures with B-metric.
result Several geometric properties and special classes are obtained.
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 .
Study weak -K-contact manifolds, finding Einstein-type metrics and solitons.
problem Characterize and study geometric properties of weak -K-contact manifolds.
method Analyzing weak metric -structures, using Killing vector fields, and Jacobi operators.
result Einstein weak -K-contact manifolds are Ricci flat.
The paper explores generalized Riemannian manifolds with weak metric structures.
problem Understanding weak metric structures on generalized Riemannian manifolds.
method Study of generalized metric connections, weak metric structures, and skew-symmetric torsion.
result Generalized Riemannian manifolds can be split into nearly Kähler manifolds.
Study --Ricci solitons on weak Kenmotsu -manifolds.
problem Characterize --Ricci solitons on weak Kenmotsu -manifolds.
method Adapted -Ricci tensor to weak metric -manifolds, studied the interaction with weak -Kenmotsu structure.
result Obtained new characteristics of -Einstein metrics.
Survey of weak metric f-manifolds, generalizing K. Yano's structures.
problem Generalizing K. Yano's f-structures to new types of manifolds.
method Exploring new structures and properties of weak metric f-manifolds.
result New applications in geometry, including Killing vector fields and Ricci-type solitons.
New metric structures generalize Sasakian and cosymplectic structures, proving rigidity and finding conditions.
problem Generalizing Sasakian and cosymplectic structures to new metric structures.
method Introducing weak structures and proving rigidity of Sasakian structures.
result Any weak Sasakian structure is homothetically equivalent to a Sasakian structure.
New structures defined for studying contact foliations and their geometry.
problem Understanding dynamics of contact foliations and their applications.
method Define and study weak nearly S- and weak nearly C-structures.
result Characterize weak nearly S- and weak nearly C- submanifolds in weak nearly Kähler manifolds.
Weak quasi contact metric manifolds and new characteristics of K-contact and Sasakian manifoldsmath.DG
Study weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.
problem Generalize K-contact and Sasakian manifolds criteria using weak quasi contact metric manifolds.
method Study weak quasi contact metric manifolds and generalize theorems for K-contact and Sasakian manifolds.
result Provide new criterions for K-contact and Sasakian manifolds in terms of curvature tensor and geometric objects.
Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.
problem Characterizing Einstein metrics in weak β-Kenmotsu manifolds.
method Adapted -Ricci tensor to weak almost contact manifolds and studied its interaction with weak β-Kenmotsu structures.
result New characteristics of Einstein metrics obtained.
The paper explores new connections in non-symmetrical gravitational theory using weak metric structures.
problem Investigating linear connections in non-symmetrical gravitational models.
method Study of generalized Riemannian manifolds with weak metric structures and connections satisfying specific conditions.
result Proved properties of connections and structures in generalized Riemannian manifolds.
Study the geometry of weak para-f-structures and subclasses.
problem Understand the geometry of weak para-f-structures and their subclasses.
method Express covariant derivative of f, prove Killing characteristic vector fields, show foliations, and demonstrate rigidity.
result Prove that characteristic vector fields are Killing and ker f defines a totally geodesic foliation.
Study explores weak generalized K-contact structures in contact metric spaces.
problem Exploring weak generalized K-contact structures in contact metric spaces.
method Introducing a weak condition and proving existence of K-contact and -structures.
result Existence of K-contact and -structures under certain conditions on the Boeckx invariant.
We study weakened -structures on manifolds, generalizing classical results.
problem Classical -structures and their properties on manifolds.
method Introduced and studied weakened -structures, subclasses, and their properties.
result Generalized known results on globally framed -manifolds.
The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.
problem Characterizing Sasakian manifolds using a new structure.
method Study of weak nearly Sasakian structures and proving theorems.
result Provides a new criterion for a weak almost contact metric manifold to be Sasakian.
Study of -Ricci solitons and -Einstein metrics on weak -Kenmotsu -manifolds.
problem Exploring new -structures and their properties in geometric settings.
method Analysis of weak -Kenmotsu -manifolds and their properties under -Ricci soliton structures.
result Weak -Kenmotsu -manifolds with and -Ricci soliton structures are -Einstein manifolds of constant scalar curvature.
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…
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.
Paper investigates conditions for independence of weak gradients on metric spaces.
problem Dependence of weak gradients on in arbitrary metric measure spaces.
method Investigates the Bounded Interpolation Property to ensure independence of weak gradients.
result Bounded Interpolation Property guarantees independence of weak gradients.
Survey of recent results in weak almost contact structures.
problem New geometric structures replacing complex structure in contact manifolds.
method Survey of recent findings in weak almost contact manifolds.
result Recent results on geodesic and Killing fields, rigidity and splitting theorems, etc.
The paper studies a new structure on contact manifolds and its foliation properties.
problem Investigating a new structure on contact manifolds.
method Examining weak nearly Sasakian structures and their foliations.
result The weak nearly Sasakian structure foliates into two types of totally geodesic foliations.
Study curvature properties of w.a. S-manifolds with new conditions.
problem Curvature properties of weak almost S-manifolds.
method Partial Ricci flow, additional conditions, f-(κ,μ)-nullity.
result Characterize S-manifolds as limits of w.a. S-manifolds.
Study on a new type of manifolds that generalize almost C-manifolds.
problem Understanding weak nearly C-manifolds and their properties.
method Analyzing conditions for local Riemannian product structures and characterizing specific dimensions.
result Conditions for a weak nearly C-manifold to become locally a Riemannian product and characterization of specific dimensions.
Compactifies Calabi-Yau to weak Fano manifolds.
problem Compactifying Calabi-Yau manifolds to weak Fano manifolds.
method Generalized Tian-Yau construction and asymptotically Calabi metrics.
result Calabi-Yau structure arises from compactification.
Study validates Michor-Mumford conjecture in infinite dimensional Hilbertian H-type groups.
problem Validation of Michor-Mumford conjecture in infinite dimensional Hilbertian H-type groups.
method Introduced infinite dimensional Hilbertian H-type groups with weak, graded, left invariant Riemannian metrics and proved the vanishing of geodesic distance and local unboundedness of sectional curvature.
result Validation of Michor-Mumford conjecture linking geodesic distance vanishing to local unboundedness of sectional curvature.
We prove that the L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold induces a metric space structure. As the L^2 metric is a weak Riemannian metric, this fact does not follow from general results. In addition, we prove several results on the exponentia…
Introduces a new geometric structure for statistical manifolds with degenerate metrics.
problem Degenerate metrics in statistical manifolds affect geometric structures and applications.
method Introduces quasi-Codazzi structure for degenerate metrics and coherent tangent bundles.
result Generalizes geometric structures and relations for statistical models with degenerate metrics.
In this paper, we study the weak compactness of the set of conformal metrics in any Riemann surface without boundary whose Calabi energy and area are uniformly bounded. We prove that for any sequence of such metrics, there alwasy exists a subsequence which converges in H\sp{2,2}_\sb{loc} everywhere except a finite numb…
In this paper, we prove that the transverse Mabuchi K-energy functional is convex along the weak geodesic in the space of Sasakian metrics. As an application, we obtain the uniqueness of constant scalar curvature Sasakian metrics modulo automorphisms for the transverse holomorphic structure.
Paper proves collapsing result for orbifolds without curvature bounds.
problem Proving collapsing result for orbifolds without curvature bounds.
method Introduces weak submersions and stratified Riemannian metrics.
result Allows Gromov-Hausdorff limits of orbifolds with strictly lower dimension.
Study on unique spacetime extensions in 1+1 dimensions with applications to weak null singularities.
problem Understanding unique spacetime extensions across null boundaries in 1+1 dimensions.
method Analyzing the - and -structures of continuous spacetime extensions.
result Extensions can have the same -structure but different -structures.
Study weak geodesic lines in Kähler metric space, disproving a conjecture.
problem Disproving a conjecture about weak geodesic lines in Kähler metrics.
method Establish Ross-Witt Nyström correspondence, construct weak geodesic lines.
result Some weak geodesic lines are smooth, disproving a popular conjecture.
We define and study metrics and weak metrics on the Teichmueller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined m…
We study the space of Riemannian metrics with positive scalar curvature on a compact manifold with boundary. These metrics extend a fixed boundary metric and take a product structure on a collar neighbourhood of the boundary. We show that the weak homotopy type of this space is preserved by certain surgeries on the bou…
Study curvature of piecewise metrics using moving frames.
problem Deriving a curvature measure for piecewise-smooth Riemannian metrics.
method Used moving frame techniques to derive curvature, showing it satisfies Cartan structure equations and gauge transformation law.
result Equivalence of the derived curvature to existing densitized distributional curvature.
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.
In this paper, we study general -metrics which is a Riemannian metric and is an one-form. We have proven that every weak Landsberg general -metric is a Berwald metric, where is a closed and conformal one-form. This show that there exist no generalized unicorn metric in this class of general $(…
Introduces a new framework for Riemannian diffeology.
problem No specific problem stated; focuses on a new framework.
method Uses tangent functor and metric from Iglesias-Zemmour to establish weak Riemannian diffeological spaces.
result Establishes a category of weak Riemannian diffeological spaces and shows induced pseudodistance is a distance under technical conditions.
A GL(2, R) structure on an (n+1)-dimensional manifold is a smooth pointwise identification of tangent vectors with polynomials in two variables homogeneous of degree n. This, for even n=2k, defines a conformal structure of signature (k, k+1) by specifying the null vectors to be the polynomials with vanishing quadratic …
Formalizes weak and strong verification for LLMs, controlling errors without assumptions.
problem Balancing cost and reliability in reasoning with LLMs.
method Formalizes weak-strong verification policies, introduces metrics, develops online algorithm.
result Optimal policies admit a two-threshold structure, and calibration and sharpness govern value of weak verifiers.
We prove certain weak or idealized existence results for minimizers of the natural quadratic curvature functionals on the space of metrics on 4-manifolds. Overall, we try to exhibit the relations with the picture in 3-dimensions provided by Thurston geometrization. The existence results apply in particular to the struc…
Tensoring -weak differentiable structures preserves their properties.
problem Tensorization of -weak differentiable structures.
method Proving the product of -weak charts is a -weak chart, and showing isometric embeddings.
result Tensorization of -weak differentiable structures is possible under certain conditions.
This paper explores integrability conditions for generalized metrics and structures on manifolds.
problem Investigating integrability conditions for generalized metrics and structures on manifolds.
method Considered two notions of integrability: Courant bracket and connection-induced bracket. Provided sufficient criteria for integrability.
result Sufficient criteria for integrability of generalized metrics and structures are formulated.
Solves geometric problems using fully nonlinear equations and Morse theory.
problem Geometric problems, specifically Loewner-Nirenberg and Yamabe problems.
method Investigates structure of fully nonlinear equations and applies Morse theory techniques.
result Constructs admissible metrics under weak conditions and demonstrates topological obstructions.
Study weak super Ricci flow through neckpinch in metric measure spaces.
problem Understanding Ricci flow behavior at singularities.
method Introduce weak super Ricci flow and show conditions for continuation.
result Weak super Ricci flow properties at singularities.
Weak Minkowski Spacesmath.DG
We define the notion of weak Minkowski metric and prove some basic properties of such metrics. We also highlight some of the important analogies between Minkowski geometry and the Funk and Hilbert geometries.