In this paper we prove that for a complete, connected and oriented Käler affine manifold of dimension if it is Kähler affine Ricci flat or the Khler affine scalar curvature (), then the universal covering manifold of is isometric to the Euclidean n-space $…
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 “Ricci-flat Kähler metric”
Study properties of para-Kähler manifolds with conformal Einstein soliton metrics.
problem Properties of para-Kähler manifolds with conformal Einstein soliton metrics.
method Investigated curvature properties of para-Kähler manifolds admitting conformal Einstein soliton.
result Certain curvature properties of para-Kähler manifolds were studied.
The paper studies Ricci curvature on Kähler-Ricci flow.
problem Analyzing Ricci curvature on Kähler-Ricci flow.
method Examining n-dimensional compact Kähler manifolds with semi-ample canonical line bundles under Kähler Ricci Flow.
result Ricci curvature converges to negative of generalized Kähler Einstein metric locally away from singular set.
New ALE Kähler metrics found on weighted projective spaces.
problem Finding scalar-flat Kähler metrics on weighted projective spaces.
method Constructing explicit toric scalar-flat Kähler ALE metrics.
result Smooth extremal Kähler metrics obtained on resolutions of orbifolds.
The paper proves conditions for Kähler manifolds with negative curvature.
problem Conditions for existence of Kähler-Einstein metrics and holomorphic curves.
method Analyzes compact Kähler manifolds homotopic to negatively curved Riemannian manifolds.
result Compact Kähler manifolds with negative curvature admit Kähler-Einstein metrics of general type.
The paper explores metric reduction in generalized geometry and constructs holomorphic bundles.
problem Metric reduction in generalized geometry and constructing holomorphic bundles.
method Investigation of Bismut connections and construction of metric generalized principal bundles.
result Construction of a family of generalized holomorphic line bundles over .
Holomorphic Euler number vanishes for certain Kähler manifolds.
problem Finding obstructions for Kähler manifolds with specific curvature properties.
method Vanishing theorem of Dolbeault-Morse-Novikov cohomology.
result Holomorphic Euler number of Kähler manifolds with almost nonnegative Ricci curvature vanishes.
Positive scalar curvature implies small 2-systoles in Kähler manifolds
problem Finding topologically non-trivial 2-spheres with small area in Kähler manifolds
method Using index theoretic methods
result Quantitative upper bounds on the 2-systole
Paper shows non-CSC HCMU metrics can't be isometrically immersed into 3D space forms.
problem Non-CSC HCMU metrics cannot be isometrically immersed into 3D space forms.
method Using moving frames to demonstrate the impossibility of isometric minimal immersion.
result Non-CSC HCMU metrics cannot be isometrically immersed into 3D space forms.
Continuity of complex Monge-Ampère potentials on Kähler manifolds.
problem Continuity of solutions to complex Monge-Ampère equations on compact Kähler manifolds.
method Extending DiNezza-Lu's approach to big cohomology classes, proving continuity on Zariski open sets.
result Singular Kähler-Einstein metrics have continuous potentials on the ample locus outside of the non-klt part.
Two conjectures on Ricci-flat metrics verified under specific conditions.
problem Properties of Ricci-flat metrics on complex manifolds.
method Analyzing conjectures and verifying them under specific conditions.
result Conjectures verified for certain types of metrics on complex surfaces.
Some Ricci-Flat -Metricsmath.DG
The paper finds equations for Ricci-flat Finsler metrics.
problem Characterizing Ricci-flat -metrics.
method Defined -metrics and found an equation for Ricci-flatness.
result Equations for Ricci-flat -metrics.
K{ä}hler geometry of horosymmetric varieties, and application to Mabuchi's K-energy functionalmath.DG
Develops Kähler geometry on new varieties for canonical metrics.
problem No specific problem stated; focuses on new varieties.
method Introduces new varieties, develops Kähler geometry, associates convex functions with metrics.
result Provides expression for Mabuchi functional and combinatorial sufficient condition of properness.
Study on compact complex manifolds with specific metrics.
problem Geometry of compact complex manifolds with Levi-Civita Ricci-flat metrics.
method Analysis of compact complex surfaces and their properties.
result Compact complex surfaces with Levi-Civita Ricci-flat metrics are either Kahler Calabi-Yau surfaces or Hopf surfaces.
New metrics found on non-Kähler Calabi-Yau manifolds.
problem Constructing Ricci-flat metrics on non-Kähler Calabi-Yau manifolds.
method Using -Gauduchon metrics on principal torus bundles over rational homogeneous varieties.
result Examples of new metrics on non-Kähler Calabi-Yau manifolds.
New methods find Ricci-flat metrics on specific Lie groups.
problem Finding Ricci-flat metrics on Lie groups.
method Two constructions based on gradings and filtrations.
result Every nilpotent Lie algebra of dimensions up to 9 admits an indefinite Ricci-flat metric.
New structures on symplectic manifolds derived from convex functions and matrices.
problem Investigating new types of toric generalized Kaehler structures on compact manifolds.
method Characterizing structures by triples , proving canonical structures, and showing reversibility.
result Underlying each structure is a canonical toric Kähler structure with a symplectic potential given by .
For the sake of hyperk{ä}hler SYZ conjecture, finding holomorphic Lagrangian fibrations becomes an important issue. Toric hyperk{ä}hler manifolds are real dimension non-compact hyperk{ä}hler manifolds which are quaternion analog of toric varieties. The dimensional residue circle action on it admitting a hyperk…
New method constructs Ricci-flat metrics on Lie groups.
problem Finding Ricci-flat metrics on Lie groups.
method Combinatorial method to construct indefinite Ricci-flat metrics.
result Infinite families of Ricci-flat nilmanifolds constructed.
New Ricci flat Kähler metrics found on complex symmetric spaces.
problem Finding Ricci flat Kähler metrics on complex symmetric spaces.
method Using an explicit asymptotic model with interpretation of geometry at infinity in the wonderful compactification.
result Obtained new Ricci flat Kähler metrics on complex symmetric spaces of rank two.
Study stability and instability of Ricci-flat metrics under generalized Ricci flow.
problem Stability and instability of Ricci-flat metrics under Ricci flow.
method Analysis of generalized Ricci flow for Ricci-flat metrics and vanishing 3-forms.
result Dynamical stability and instability results for Ricci-flat metrics and vanishing 3-forms.
Survey on metric behavior of Kähler-Einstein metrics during Calabi-Yau degenerations.
problem Metric behavior of Kähler-Einstein metrics during Calabi-Yau degenerations.
method Survey of recent progress.
result Recent insights into metric behavior during Calabi-Yau degenerations.
This paper classifies minimal complex surfaces with Levi-Civita Ricci-flat metrics.
problem Classifying minimal complex surfaces with specific geometric properties.
method Study of compact complex manifolds with Levi-Civita Ricci-flat metrics.
result Minimal complex surfaces with Levi-Civita Ricci-flat metrics are Kähler Calabi-Yau surfaces and Hopf surfaces.
Continuous family of Ricci-flat metrics found on complex projective spaces.
problem Finding invariant Ricci-flat metrics with specific properties.
method Constructing a 1-parameter family of smooth complete metrics on vector bundles over complex projective spaces.
result Continuous family of Ricci-flat metrics with generic holonomy, including a metric.
The paper constructs flat metrics on orbifolds and resolutions.
problem Finding flat metrics on orbifolds and their resolutions.
method Gluing construction and analysis of singularities.
result All crepant resolutions of non-Kähler Calabi-Yau orbifolds with Chern-Ricci flat balanced metrics admit such metrics.
Simply connected moduli space of Ricci flat metrics on K3 surfaces.
problem Understanding the topology of Ricci flat metrics on K3 surfaces.
method Analyzing the moduli space of metrics with unit volume.
result The moduli space is simply connected and has cohomology matching the automorphism group.
Researchers describe invariant Ricci-flat Kähler metrics on tangent bundles of symmetric spaces.
problem Finding all invariant Ricci-flat Kähler metrics on tangent bundles of compact symmetric spaces.
method Using special local vector fields to describe metrics on .
result Explicit description of complete -invariant metrics on .
Study on Calabi-Yau metrics and their degenerations.
problem Understanding degenerations of Ricci-flat Kahler metrics on Calabi-Yau manifolds.
method Survey of recent results on questions about degenerations.
result Survey of recent results on degenerations of metrics.
Study on how incomplete smooth metrics degenerate from asymptotically conical Ricci-flat Kähler metrics.
problem Degeneration of asymptotically conical Ricci-flat Kähler metrics.
method Analysis of Kähler class degeneration and convergence of metrics.
result Construction of singular Calabi-Yau metrics and their metric geometry.
The paper classifies special nilpotent Lie groups with Ricci-flat and Einstein metrics.
problem Finding metrics on nilpotent Lie groups that are both Ricci-flat and Einstein.
method Classification of metrics using a new criterion for diagonal Einstein metrics.
result Classifications of Ricci-flat metrics on nilpotent Lie groups of dimension ≤8.
Study K3 surfaces and their metrics, focusing on dynamics.
problem Understanding dynamics on K3 surfaces.
method Interactions between K3 surface geometry and Ricci-flat metrics, dynamical study of automorphisms.
result Positive entropy automorphisms on K3 surfaces.
Study of Ricci-flat metrics on manifolds, showing rigidity in their holonomy.
problem Understanding the structure of Ricci-flat metrics on manifolds.
method Analyzing the space of all Riemannian metrics admitting non-zero parallel spinors on the universal covering.
result Holonomy group is locally constant on the space of such metrics.
Explicitly describes Ricci-flat Kähler metrics on tangent bundles of symmetric spaces.
problem Finding Ricci-flat Kähler metrics on tangent bundles of symmetric spaces.
method Explicit description using invariant vector-functions.
result Complete -invariant Ricci-flat Kähler metrics on are explicitly given.
Study shows Ricci flat Calabi's metrics can't be projectively induced.
problem Characterizing metrics that can be induced projectively.
method Analyzing Ricci flat Calabi's metrics on specific manifolds.
result Ricci flat Calabi's metrics are not projectively induced.
Study on stability of ALE Ricci-flat metrics using a modified Perelman's λ-functional.
problem Stability and instability of ALE Ricci-flat metrics.
method Use of a modified Perelman's λ-functional and Lojasiewicz inequality.
result Demonstrates dynamical instability of ALE Ricci-flat metrics.
We prove that a crepant resolution of a Ricci-flat Kähler cone X admits a complete Ricci-flat Kähler metric asymptotic to the cone metric in every Kähler class in H^2_c(Y,R). This result contains as a subcase the existence of ALE Ricci-flat Kähler metrics on crepant resolutions of X=C^n /G, where G is a finite subgroup…
We determine all Ricci flat left invariant Lorentzian metrics on simply connected 2-step nilpotent Lie groups. We show that the -dimensional Heisenberg Lie group carries a Ricci flat left invariant Lorentzian metric if and only if . We show also that for any , carries a R…
Constructs Ricci-flat metrics on vector bundles over flag manifolds.
problem Finding explicit complete Ricci-flat metrics on vector bundles over flag manifolds.
method Explicit construction of metrics on vector bundles over flag manifolds of SU(n).
result Natural generalizations of known metrics on specific bundles.
Constructs Einstein metrics on manifolds with specific orbits.
problem Finding Einstein metrics on manifolds with given orbits.
method Continuous families of metrics constructed using vector bundles and .
result Recovery of metrics and .
Conditions ensure Ricci-flat metrics on certain 4-manifolds.
problem Ensuring Ricci-flat metrics on specific 4-manifolds.
method Topological conditions for spin and A-hat genus, large cardinality of fundamental group.
result Sufficient conditions for existence of Ricci-flat metrics.
The paper constructs a new Ricci-flat metric on almost abelian Lie groups.
problem Finding Lorentzian homogeneous Ricci-flat metrics on almost abelian Lie groups.
method Constructing left-invariant metrics on almost abelian Lie groups, focusing on dimensions four or higher.
result A new Ricci-flat metric that generalizes the Petrov solution to higher dimensions.
Researchers describe a method to construct Ricci-flat metrics on a specific surface.
problem Constructing Ricci-flat metrics on a del Pezzo surface.
method Developed a framework and explicitly constructed the first-order deformation of the orthotoric metric.
result The deformation of the conformal Killing-Yano form does not exist.
Proves orbifold singularities for Ricci-flat metrics on certain Kähler varieties.
problem Regularity of singular Ricci-flat Kähler metrics on Kähler varieties with log terminal singularities.
method Analyzes orbifold singularities of metrics restricted to the orbifold locus.
result Singular Ricci-flat Kähler metrics on Kähler varieties with log terminal singularities have orbifold singularities.
The paper proves volume comparison theorems for metrics near stable Einstein and Ricci flat manifolds.
problem Investigating volume comparison theorems for metrics near stable Einstein and Ricci flat manifolds.
method Applying similar techniques to derive local rigidity theorems for strictly stable Ricci flat manifolds.
result Derives local rigidity theorems for strictly stable Ricci flat manifolds with respect to σ2-curvature.
We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled metrics on the fibers converge to Ricci-flat Kahler metrics. This strengthens previous…
Classifies Einstein metrics on R^4 with Heisenberg symmetry, finding incomplete Ricci-flat metrics and two complete negative-curvature examples.
problem Classifying Einstein metrics on with Heisenberg symmetry.
method Invariant under a four-dimensional group of isometries including the Heisenberg group, analyzing Ricci-flat and negative-curvature metrics.
result Found two complete negative-curvature examples: complex hyperbolic metric and one-loop deformed universal hypermultiplet.
Using methods of A. Grigor'yan and L. Saloff-Coste we prove that on a manifold with a conical end the heat kernel has a Gaussian bound. This result is applied to asymptotically conical Kähler manifolds. It is a result of the author and R. Goto that a crepant resolution of a Ricci-flat Kähler cone admits a Ricci-flat Kä…
In this note, we obtain existence results for complete Ricci-flat Kahler metrics on crepant resolutions of singularities of Calabi-Yau varieties. Furthermore, for certain asymptotically flat Calabi-Yau varieties, we show that the Ricci-flat metric on the resolved manifold has the same asymptotic behavior as the initial…