We prove a Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds with asymptotic geometry at infinity. The asymptotic geometry at infinity is either a cusp bundle over a compact space (the fibered cusps) or a fiber bundle over a cone with a compact fiber (the fibered boundary). Many noncompact Einstein manifold…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “fibered geometry”
Study variations of metrics on Riemannian submersions to preserve fiber geometry.
problem Preserving specific geometries of fibers under metric variations on Riemannian submersions.
method Formulated conditions for preserving fiber geometry (totally geodesic, umbilical, minimal) and examined variations of sectional curvatures.
result Conditions for metric to be a critical point of integrated squared norms of fiber curvatures, with non-negative second variation.
Classifies 5D homogeneous geometries with nontrivial reducible linear isotropy.
problem Classifying 5D homogeneous geometries with specific properties.
method Thorough classification using Thurston's criteria and analysis of linear isotropy representations.
result Found a countably infinite family of geometries diffeomorphic to .
Study compares bundles with connections to prehomogeneous geometries.
problem Comparing bundle structures to prehomogeneous geometries.
method Analyzes fibered manifolds, jet bundles, and nonlinear PDEs.
result Identifies similarities and differences between bundle structures and prehomogeneous geometries.
Study connects surface projections in fibered 3-manifolds.
problem Understanding surface projections in fibered 3-manifolds.
method Uniformly relates structure of surface projections across fibrations.
result Extends previous work to general cases.
Establishes a principle for metric convergence in Kähler geometry.
problem Convergence of evolving Riemannian metrics in Kähler geometry.
method General 'boundedness implies convergence' principle applied to collapsing Calabi-Yau metrics and normalized Kähler-Ricci flows.
result Obtains convergence results for collapsing Calabi-Yau metrics and normalized Kähler-Ricci flows.
The Milnor fiber conjecture is proven for splice type singularities.
problem Proving the Milnor fiber conjecture for a specific class of singularities.
method Combining techniques from tropical geometry, log geometry, and rounding of logarithmic spaces.
result The Milnor fiber conjecture is proven for splice type singularities.
FiberNet integrates geometry into machine learning for clearer classification.
problem Lack of interpretability in traditional deep learning.
method Reformulates classification as geometric optimization on fiber bundles, introducing learnable Riemannian metrics and variational prototype optimization.
result Clear geometric interpretability and efficiency in classification.
Study on fibered knots in 3-manifolds, proving unrelated volume and genus.
problem Unrelated volume and genus in hyperbolic fibered knots.
method Proof of unrelated volume and genus for hyperbolic fibered knots in 3-manifolds.
result Proved that volume and genus are unrelated for hyperbolic fibered knots.
New geometry based on Siegel upper half-space with volume formula.
problem Developing a new 3D geometry based on Siegel upper half-space.
method Constructing a geometry fibered over Siegel upper half-space and providing a volume formula.
result Volume of Siegel-Seifert closed manifolds is the fiber circle length times base manifold's Euler characteristic.
Contact fiber bundlesmath.DG
We define contact fiber bundles and investigate conditions for the existence of contact structures on the total space of such a bundle. The results are analogous to minimal coupling in symplectic geometry. The two applications are construction of K-contact manifolds generalizing Yamazaki's fiber join construction and a…
In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the ``closed fibers at infinity''. Manin described the dual graph of any such closed fiber in terms of an infinite tangle of bounded geodesics in a hyperbolic handlebody endowed with …
Unified view of geometries with parallel skew torsion via submersions.
problem No de Rham decomposition for geometries with torsion.
method Developed and unified submersion constructions for geometries with parallel skew torsion.
result Completed and extended classification of irreducible geometries with parallel skew torsion.
Let X be a compact connected Kaehler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly, Peternell and Schenider says that there is a finite unramified Galois covering M --> X, a complex torus T, and a holomorphic surjective submersion f: M --> T, such that the fibers o…
The study limits the number of ribbon concordant fibered knots.
problem Understanding the relationship between ribbon concordance and fibered knots.
method Combining Floer homology results with fixed points of monodromy and volume inequalities.
result There are only finitely many hyperbolic fibered knots ribbon concordant to any given knot.
New 5D hyperbolic shapes that wrap around a circle found.
problem Finding new 5D hyperbolic structures.
method Examined finite-volume cusped hyperbolic 5-manifolds.
result Discovered the smallest known hyperbolic 5-manifold.
The paper extends a theorem to manifolds with local Ricci bounded covering geometry.
problem Understanding collapsed manifolds with specific Ricci curvature properties.
method Extending a theorem from nilpotent fiber bundles to manifolds with local -bound Ricci covering geometry.
result Manifolds with local -bound Ricci covering geometry are diffeomorphic to infra-nilmanifolds.
The paper explores how curvature positivity affects the finiteness of fundamental groups in semi-Riemannian geometry.
problem The relationship between curvature positivity and fundamental group finiteness in semi-Riemannian geometry.
method Investigation of semi-Riemannian submersions with specific conditions on curvature positivity and integrability.
result If a semi-Riemannian manifold has curvature positivity, the fundamental group of its fiber is finite.
The paper studies biharmonic submersions in Riemannian geometry.
problem Characterizing biharmonic Riemannian submersions.
method Deriving bitension field equations and using them to construct biharmonic examples and characterize submersions.
result Examples of proper biharmonic Riemannian submersions with 1-dimensional fibers and characterizations of warped products.
Study asymptotics of hyperkähler geometry on singular fibers of Hitchin moduli space.
problem Asymptotic hyperkähler geometry of -Hitchin moduli space over singular fibers.
method Extension of exponential convergence results to locally fiducial Higgs bundles and subintegrable systems.
result Hyperkähler metric converges exponentially to semi-flat metric on subintegrable systems.
In this paper, we describe a new surprising example of a fibration of the Clifford torus S3 x S3 in the 7-sphere by great 3-spheres, which is fiberwise homogeneous but whose fibers are not parallel to one another. In particular it is not part of a Hopf fibration. A fibration is fiberwise homogeneous when for any two fi…
Maps are shown to be Riemannian products with Ricci-flat fibers.
problem Understanding maps between manifolds and their geometric properties.
method Spin geometry and representation theory of curvature operators.
result Scalar-rigid maps are essentially Riemannian products of base and Ricci-flat fibers.
Study Einstein warped products with Einstein base and fiber.
problem Characterize Einstein warped products with Einstein base and fiber.
method Investigate necessary and sufficient conditions for a warped product to be Einstein.
result Explicitly determine the warping function when the base is hyperbolic space.
Lectures on link homology and its algebraic/geometric models.
problem Defining and understanding link homology.
method Definition and properties of Khovanov-Rozansky triply graded homology, and three geometric models.
result Three geometric models for link homology: braid varieties, Hilbert schemes, and affine Springer fibers.
Fibers of abelian varieties over curves can be approximated algebraically.
problem Approximating fibers of abelian varieties over curves algebraically.
method Proving the existence of algebraic approximations for fibrations.
result Fibrations with abelian varieties over curves have algebraic approximations.
We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the total space is discrete if and only if the base is di…
Overview of fiber bundles in gauge theories with visual emphasis.
problem Understanding fiber bundles and their connections in gauge theories.
method Pedagogical definitions, visualizations, and geometric viewpoints.
result Novel figures and geometric perspectives on fiber bundles.
Study of twisted Kähler-Einstein metrics on Calabi-Yau spaces with singularities.
problem Understanding the collapsed Gromov-Hausdorff limits of Calabi-Yau spaces.
method Analyzing the geometry of twisted Kähler-Einstein metrics on holomorphic fiber spaces.
result Proving the existence of conical-type singularities in the base of fiber spaces.
Study on noncompact steady quasi-Einstein manifolds with positive Ricci curvature.
problem Characterize noncompact steady quasi-Einstein manifolds with positive Ricci curvature.
method Analyze Bach-flat noncompact steady quasi-Einstein manifolds with positive Ricci curvature, proving they must be warped products with Einstein fibers.
result Warped product structure with constant curvature for 4-dimensional manifolds.
Geometric approach to quantum thermodynamics models state spaces and processes.
problem Quantum thermodynamics in the regime of non-equilibrium states.
method Contact geometry and principal fiber bundles to model quantum state spaces and processes.
result Geometric formulation reveals the fundamental thermodynamic relations and unattainability of the third law.
Study shows discrete spectra on base spaces for certain Riemannian submersions.
problem Discreteness of spectra under Riemannian submersions.
method Estimates spectrum of total space in terms of base space and fiber geometry.
result Spectrum of base space discrete if and only if spectrum of total space is discrete.
Study of spacelike hypersurfaces in twisted product spacetimes with specific conditions.
problem Characterizing and understanding spacelike hypersurfaces in twisted product spacetimes.
method Analysis of conditions ensuring global hyperbolicity, use of conformal geometry results.
result Non-existence results for constant mean curvature hypersurfaces under certain conditions.
FibeRed reduces complex data dimensions while preserving topology.
problem Hard embedding of topologically complex datasets in low-dimensional Euclidean space.
method Modeling datasets with vector bundles, reducing fibers while preserving topology.
result FibeRed learns topologically faithful embeddings in lower dimensions than existing methods.
If Pi: M -> B is an onto smooth maximal rank map between complete Riemannian manifolds M and B with bounded geometry, we prove sufficient conditions for M to be roughly isometric to the Riemannian product FxB, where F is a fiber of M.
Geometric framework for aligning fiber tracts across subjects.
problem Challenges in finding direct tract correspondence across multiple individuals.
method Geometric framework using intrinsic mean and deformation fields, parallel transport for registration.
result Bundle alignment results on 43 healthy adult subjects.
Improved bounds linking entropy and volume in hyperbolic 3-manifolds.
problem Establishing bounds between entropy and volume in hyperbolic 3-manifolds.
method Heegaard Floer homology and hyperbolic geometry.
result Entropy is bounded by hyperbolic volume with logarithmic factor.
Linear progress in fibresmath.GT
Linear progress observed in fibered 3-manifold embeddings.
problem Understanding the geometric distortion of fibered embeddings.
method Verification of linear progress along typical rays using geometry and ergodic theory.
result A typical ray in the fiber makes linear progress in the ambient metric.
Uniform diameter bounds for Calabi-Yau fibrations with singular fibers.
problem Bounding the diameter of Calabi-Yau fibrations near singular fibers.
method Uniform diameter bound proof for Calabi-Yau fibrations with canonical singular fibers.
result Uniform diameter bounds for all fibres in suitable rescaling.
Hyperkähler reduction explained via frame bundles.
problem Describing hyperkähler reduction using frame bundles.
method Using frame bundles and connections, tracing reductions and analyzing fibers.
result Fibers of hyperkähler reduction are totally geodesic.
The study examines pseudo-Anosov maps on curve complexes and their asymptotic translation lengths.
problem Analyzing the behavior of pseudo-Anosov maps on curve complexes.
method Using sequences of fibers and monodromies in the fibered cone, the asymptotic translation length of pseudo-Anosov maps is studied.
result The asymptotic translation length of pseudo-Anosov maps on curve complexes behaves asymptotically like .
Study collapsing Calabi-Yau metrics and flows on fiber spaces.
problem Understanding the behavior of Calabi-Yau metrics and flows during collapsing.
method Analyzing the collapsing of Calabi-Yau metrics and Kähler-Ricci flows on fiber spaces.
result Identify the collapsed Gromov-Hausdorff limit and bounds for Hausdorff measure.
New singularity theorems for warped products help analyze extra dimensions stability.
problem Stability of extra dimensions in warped product spacetimes.
method Derived new singularity theorems for warped-product spacetimes, analyzed conditions for geodesic incompleteness, and solved conditions for parallel transportation.
result Explicit conditions on the warping function that lead to geodesic incompleteness, providing insights into the intrinsic geometry of extra dimensions.
In this short note, we show that given a special Kähler-Einstein degeneration with bounded geometry, for any noncentral fiber, there exists a Kähler-Ricci flow which converges to the Kähler-Einstein metric of the central fiber. As an example, Tian's deformations \cite{Tian97} of the Mukai 3-fold admit Kähler-Ricci flow…
In present paper, the equivalence problem for fourth order differential operators with one variable under general fiber-preserving transformation using the Cartan method of equivalence is applied. Two versions of equivalence problems are considered. First, the direct equivalence problem and second equivalence problem i…
Nonlinear soft-tissue elasticity, remodeling, and degradation described by an extended Finsler geometrycond-mat.soft
Theory models nonlinear soft tissue elasticity and remodeling using extended Finsler geometry.
problem Understanding and predicting the behavior of nonlinear soft tissues, especially in biologic contexts.
method Formulated a continuum mechanical theory incorporating extended Finsler geometry to describe the complex behaviors of fibrous soft solids.
result The model quantifies residual strains from growth, remodeling, and degradation, and predicts equilibrium configurations.
Calibrated Fibrationsmath.DG
In this paper we investigate the geometry of Calibrated submanifolds and study relations between their moduli-space and geometry of the ambient manifold. In particular for a Calabi-Yau manifold we define Special Lagrangian submanifolds for any Kahler metric on it. We show that for a choice of Kahler metric the Borcea-V…
New Sasaki metrics with constant scalar curvature on sphere bundles are constructed.
problem Constructing extremal Sasaki metrics with constant scalar curvature.
method Using the fiber join construction and a recent existence theorem for constant scalar curvature Sasaki metrics.
result Explicit constructions of constant scalar curvature Sasaki metrics on specific sphere bundles.
Mathematical theory of super fiber bundles and connections developed.
problem Modeling anticommuting fermionic fields in mathematical physics.
method Detailed introduction to super fiber bundles, relative supermanifolds, and connections; construction of parallel transport map.
result Construction and comparison of parallel transport map with other methods in the literature.