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 $C$-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.
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.
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.
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 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.
Weak -Dirac manifoldsmath.DG
Introduces weak -Dirac structures in geometric settings.
problem Defining and analyzing new geometric structures.
method Introducing and studying weak -Dirac structures in .
result Weak -Dirac structures contain more information than -Lagrangian structures.
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.
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.
The study examines conditions for weak nearly cosymplectic manifolds to split into products.
problem Understanding the curvature and topology of weak nearly cosymplectic manifolds.
method Analyzes the conditions for splitting and characterizes specific manifolds.
result Conditions for weak nearly cosymplectic manifolds to become Riemannian products are identified.
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 .
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.
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.
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.
This paper proves that one-relator groups have a weak Z-structure.
problem The existence of weak Z-structures for all groups of type F.
method Analyzing the geometric properties of one-relator groups and their boundaries.
result Torsion-free one-relator groups have a weak Z-structure.
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.
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.
We detail the construction of a weak Poisson bracket over a submanifold of a smooth manifold M with respect to a local foliation of this submanifold. Such a bracket satisfies a weak type Jacobi identity but may be viewed as a usual Poisson bracket on the space of leaves of the foliation. We then lift this weak Poisson …
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.
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 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.
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.
We are concerned with the global weak continuity of the Cartan structural system -- or equivalently, the Gauss--Codazzi--Ricci system -- on semi-Riemannian manifolds with lower regularity. For this purpose, we first formulate and prove a geometric compensated compactness theorem on vector bundles over semi-Riemannian m…
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.
Motivated by the usefulness of boundaries in the study of hyperbolic and CAT(0) groups, Bestvina introduced a general approach to group boundaries via the notion of a Z-structure on a group G. Several variations on Z-structures have been studied and existence results have been obtained for some very specific classes of…
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.
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.
Weak dual pairs defined in Dirac-Jacobi geometry, proving equivalence and leaf correspondence theorems.
problem Defining and studying weak dual pairs in Dirac-Jacobi structures.
method Adopting omni-Lie algebroid approach, proving equivalence and leaf correspondence theorems.
result Existence of self-dual pairs and alternative proof of normal form theorem.
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.
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.
We introduce a notion of a weak Poisson structure on a manifold modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra $\cA \subeq C^\infty(M)$ which has to satisfy a non-degeneracy condition (the differentials of elements of $\cA$ separate tangent vectors) and we postulate …
Weak Correlations as the Underlying Principle for Linearization of Gradient-Based Learning Systemscs.LG
Weak correlations explain linear dynamics in deep learning models.
problem Understanding the linear structure in gradient-based learning algorithms.
method Characterization of weak correlations between derivatives and parameters.
result Weak correlations are the underlying principle for linearization in deep learning models.
Labeling training data is a key bottleneck in the modern machine learning pipeline. Recent weak supervision approaches combine labels from multiple noisy sources by estimating their accuracies without access to ground truth labels; however, estimating the dependencies among these sources is a critical challenge. We foc…
We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic …
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.
Translating renderings (e. g. PDFs, scans) into hierarchical document structures is extensively demanded in the daily routines of many real-world applications. However, a holistic, principled approach to inferring the complete hierarchical structure of documents is missing. As a remedy, we developed "DocParser": an end…
Optimizes shapes on non-standard manifolds.
problem Optimization on non-standard infinite-dimensional manifolds.
method Develops gradient descent on weak Riemannian manifolds.
result Establishes foundational properties for optimization on various weak Riemannian manifolds.
Develops Poisson structures on weak Sobolev loop spaces for integrable systems.
problem Analyzing integrable systems on low regularity loop spaces.
method Extending Mokhov's constructions to weak Sobolev spaces, constructing presymplectic and Poisson structures.
result Valid Poisson structures and deformations for weak Sobolev loops, extending Hamiltonian formalisms.
New Lie 2-algebra structure for multiplicative forms on quasi-Poisson groupoids.
problem Understanding Lie 2-algebra structures on geometric stacks.
method Construction of graded weak Lie 2-algebras from multiplicative forms and differential forms.
result Established a morphism between Lie 2-algebras and weak Lie 2-algebras of multiplicative forms.
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.
Develops analysis of weak immersions with bounded second fundamental forms in critical Sobolev space.
problem Analyzing weak immersions with bounded second fundamental forms in a critical Sobolev space.
method Develops analysis of Lipschitz immersions with bounded second fundamental forms in space.
result Proves existence of differential structure from weak immersions with bounded second fundamental forms.
We present the extended Kuranishi space for Kodaira surface as a non-trivial example to Kontsevich and Barannikov's extended deformation theory. We provide a non-trivial example of Hertling-Manin's weak Frobenius manifold. In addition, we find that Kodaira surface is its own mirror image. Our computation is done in the…
New methods lift weak supervision to structured prediction, providing robustness guarantees.
problem Applying weak supervision techniques to structured prediction problems.
method Introducing pseudo-Euclidean embeddings, tensor decompositions, and invariants for consistent noise rate estimation.
result Generalization guarantees nearly identical to those for models trained on clean data.
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.
Estimates long-term effects using past experiments as instruments with many weak instruments.
problem Estimating long-term causal effects with limited short-term outcomes and many weak instruments.
method Nonparametric instrumental variable inference with many weak instruments, using past experiments as instruments.
result Automatic debiased machine learning estimators for linear functionals of the structural function and its minimum-norm projection are efficient in the many-weak-instruments regime.
Weak diffusion priors can still perform well in inverse problems.
problem Using mismatched or low-fidelity diffusion priors in inverse problems.
method Extensive experiments and theoretical analysis combining Bayesian-consistency theory and local-correlation analysis.
result Weak priors succeed when measurements are highly informative, and they fail in other regimes.
Control data constructed for smooth weak deformation retraction of stratified spaces.
problem Construct control data for smooth weak deformation retraction of stratified spaces.
method Show smooth local triviality with conical fibers, construct control data, use fiber-wise scalar multiplications.
result Obtain neighbourhood smooth weak deformation retraction of stratified spaces.
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.