We find necessary and sufficient conditions for a Riemannian four-dimensional manifold with anti-self-dual Weyl tensor to be locally conformal to a Ricci--flat manifold. These conditions are expressed as the vanishing of scalar and tensor conformal invariants. The invariants obstruct the existence of parallel …
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 “anti-self-dual Ricci-flat manifolds”
The paper constructs examples of complex manifolds with singularities and jumps.
problem Understanding the structure and behavior of complex manifolds with singularities.
method Explicit construction of twistor spaces with jumping rational curves and singularities.
result The existence of normalisable solutions through folds in certain cases.
Study on harmonic forms on K3 surfaces converging to a flat 4D orbifold.
problem Behavior of harmonic 2-forms on K3 surfaces with Ricci-flat metrics.
method Analysis of convergence of harmonic forms to flat 4D orbifold.
result Decomposition of harmonic 2-forms into converging subspaces.
Using twistor methods, we explicitly construct all local forms of four--dimensional real analytic neutral signature anti--self--dual conformal structures with a null conformal Killing vector. We show that is foliated by anti-self-dual null surfaces, and the two-dimensional leaf space inherits a natural pr…
Study on type-D Ricci-flat metrics with Killing spinors and Killing vectors.
problem Characterizing and solving metrics with specific properties.
method Using Killing spinors and Killing vectors, rederive results via Toda field equations and axisymmetric solutions.
result Field equations linearize for certain metrics, including axisymmetric solutions.
The abstract conjectures and proves conditions for scalar-flat Kähler surfaces with specific tensor properties.
problem Conditions for scalar-flat Kähler surfaces with special tensor properties.
method Conjecture and prove in three special cases.
result The conjecture is proven in three special cases.
In this note we prove that any four-dimensional half conformally flat gradient steady Ricci soliton must be either Bryant's soliton or Ricci flat. We also classify four-dimensional half conformally flat gradient shrinking Ricci solitons with bounded curvature.
Constructing Einstein analogues with a non-zero cosmological constant
problem Constructing an Einstein analogue with a non-zero cosmological constant
method Proving the solution is either the Plebański-Demiański metric or has an anti-self-dual Weyl tensor
result For λ < 0, there is a conformal infinity separating two asymptotically hyperbolic metrics; one is globally conformal to an ALE scalar-flat Kähler metric; gravitational instantons with different topologies are constructed; the geometry is a 4-pole solution in the Calderbank-Pedersen classification
This review discusses solutions to Einstein's equations using twistor theory.
problem Finding solutions to Einstein's vacuum equations using twistor theory.
method Holomorphic vector bundles on twistor space and patching matrices.
result Holomorphic patching matrix is simpler than the metric and determines the rod structure.
New example shows open subset of anti-self-dual metrics is not closed.
problem Understanding the structure of moduli spaces of anti-self-dual metrics.
method Link between harmonic functions on hyperbolic 3-manifolds and self-dual harmonic 2-forms.
result The subset of anti-self-dual metrics is not generally closed.
The study finds and disproves the existence of specific metrics on 4-manifolds.
problem Existence and non-existence of certain metrics on 4-manifolds.
method Deformation of scalar-flat Kahler metrics and Seiberg-Witten theory.
result Proves the non-existence of specific metrics and provides a new proof of Seiberg-Witten invariant.
We discuss the twistor correspondence between path geometries in three dimensions with vanishing Wilczynski invariants and anti-self-dual conformal structures of signature . We show how to reconstruct a system of ODEs with vanishing invariants for a given conformal structure, highlighting the Ricci-flat case in…
A classification result for Ricci-flat anti-self-dual asymptotically locally Euclidean 4-manifolds is obtained: they are either hyperkähler (one of the gravitational instantons classified by Kronheimer), or they are a cyclic quotient of a Gibbons-Hawking space. The possible quotients are described in terms of the monop…
Almost-Kähler metrics found on a specific 4-manifold.
problem Finding anti-self-dual metrics on a specific 4-manifold.
method Using twistor space to construct anti-self-dual classes, then showing existence of almost-Kähler representatives.
result Some anti-self-dual classes on have almost-Kähler representatives.
Study shows convergence of Yang-Mills connections on K3 surfaces under fiber collapse.
problem Analyzing Yang-Mills connections on K3 surfaces as fibers collapse.
method Proves convergence of a sequence of anti-self-dual connections under specific conditions.
result Connections converge to a limiting flat connection with holomorphic structure.
Anti-self-dual blowupsmath.DG
New metric found for 4-manifolds with specific properties.
problem Finding metrics on 4-manifolds with embedded spheres.
method Constructing a Riemannian metric with anti-self-dual harmonic forms.
result Existence of a metric representing a cohomology class of a sphere.
In this short note we prove that any complete four dimensional anti-self-dual (or self-dual) quasi-Einstein manifolds is either Einstein or locally conformally flat. This generalizes a recent result of X. Chen and Y. Wang.
Notions of self-dual and anti self-dual almost quaternionic structures are introduced. The complete classification of self-dual and anti self-dual generalized Kaehler manifolds is obtained.
Compactness theorems for SL(2;C) generalizations of the 4-dimensional anti-self dual equationsmath.DG
Uhlenbeck's compactness theorem can be used to analyze sequences of connections with anti-self dual curvature on principal SU(2) bundles over oriented 4-dimensional manifolds. The theorems in this paper give an extension of Uhlenbeck's theorem for sequences of solutions of certain SL(2,C) analogs of the anti-self dual …
Study contact instantons on Sasakian 5-manifolds with Calabi-Yau structures.
problem Anti-self-dual contact instantons on Sasakian 5-manifolds with transverse Calabi-Yau structures.
method Singularity data of leaf spaces and computation of moduli spaces.
result Explicit computation of complex dimensions of moduli spaces for 95 orbifold K3 surfaces.
Compact theorem for anti-self-dual equations on cylindrical manifolds.
problem Proving compactness of instantons with translation symmetry.
method Gromov-Uhlenbeck type compactness theorem for anti-self-dual instantons.
result Sequence of instantons converges to singular objects with instanton and holomorphic curve components.
New homogeneous manifolds with invariant Bismut Ricci flat connections are constructed.
problem Constructing homogeneous manifolds with invariant Bismut Ricci flat connections.
method Classification and construction of homogeneous spaces with specific properties.
result Examples of compact homogeneous Riemannian manifolds with invariant Bismut Ricci flat connections are provided.
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 study calculates harmonic functions and 1-forms on specific 4D spaces.
problem Computing harmonic functions and 1-forms on ALE Ricci-flat 4-manifolds.
method Computed the expansion of harmonic functions and 1-forms.
result Computed the expansion of harmonic functions and 1-forms on ALE Ricci-flat 4-manifolds.
Simply connected 4-manifolds with specific Weyl tensor are geodesic balls in space forms.
problem Characterizing 4-manifolds with harmonic anti-self dual Weyl tensor.
method Proving isometry to geodesic balls in space forms.
result Simply connected critical metrics are geodesic balls in space forms.
In [29], Plebanski reformulated the anti-self-dual Einstein equations with non-zero scalar curvature as a first order PDE for a connection in an SO(3)-bundle over the four-manifold. The aim of this article is to place this differential equation in a new framework, in which it is both elliptic and a stationary point of …
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.
Study describes global sections of chiral de Rham complex on compact Ricci-flat Kähler manifolds.
problem None explicitly stated; focuses on description of global sections.
method Complete description of vertex algebra of global sections.
result Complete description of vertex algebra of global sections of chiral de Rham complex.
New criterion for Ricci-flat manifolds with non-vanishing Rosenberg index.
problem Existence of parallel spinors on Ricci-flat manifolds.
method Generalization of existing results to manifolds with non-vanishing Rosenberg index.
result Every closed connected Ricci-flat spin manifold of dimension ≥ 2 with non-vanishing Rosenberg index has special holonomy.
Identifies scales in Ricci-flat manifolds at infinity.
problem Identifying between distant scales in non-compact Ricci-flat manifolds.
method Gradient flow of an elliptic equation on a tangent cone at infinity.
result Natural identification map between scales at infinity.
ALE Ricci-flat manifolds stable under Ricci flow if integrable.
problem Stability of ALE Ricci-flat manifolds under Ricci flow.
method Adapting Tian's approach for closed manifolds, proving integrability for ALE Calabi-Yau manifolds.
result ALE Ricci-flat manifolds are dynamically stable if integrable.
Study conics and their geometric properties using twistors and anti-self-dual metrics.
problem Characterize the range of the Radon transform on conics in CP^2.
method Use differential operators on and its complexification, and analyze anti-self-dual conformal structures.
result Zero loci of functions in the Radon transform range are four-manifolds with specific Kähler metrics and holomorphic fibrations.
This is the second of two papers that describe a compactness theorem for sequences of solutions of certain SL(2;C) analogs of the anti-self dual equations on oriented, 4-dimensional Riemannian manifolds. This paper proves theorems that characterize the singular locus of limits of sequences of solutions to the equations…
In this article, we prove that a quotient of a K3 surface by a free Z_2+Z_2 action does not admit any metric of positive scalar curvature. This shows that the scalar flat anti self-dual metrics (SF-ASD) on this manifold can not be obtained from a family of metrics for which the scalar curvature changes sign, contrary t…
New method for constructing gluing parameterizations in geometric analysis.
problem Constructing gluing parameterizations for anti-self-dual connections.
method Using maps of smooth Banach manifolds with corners.
result Provides a method applicable to other nonlinear PDE problems.
We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi--Yau geometry and analysis and the Kodaira--Kuranishi--Spencer theory and building up on results of N.Koiso for the case of compact manifolds, we show that under rather general hypotheses any …
Compact Lorentzian manifolds embed in Ricci-flat spaces.
problem Embedding Lorentzian manifolds in Ricci-flat semi-Riemannian spaces.
method Reviewing relevant results, constructing isometric embeddings for compact Lorentzian manifolds in Ricci-flat semi-Riemannian spaces.
result Any compact Lorentzian manifold with specific Sobolev space properties admits an isometric embedding in a Ricci-flat semi-Riemannian manifold.
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.
We study relation of the Ricci Flow on 3-dimensional Lie groups and 4-dimensional Ricci-flat manifolds. In particular, we construct Ricci-flat cohomogeneity one metrics with respect to 3-dimensional Lie groups.
Let N_0 = C^2/H be an isolated quotient singularity with H in U (2) a finite subgroup. We show that for any Q-Gorenstein smoothings of N_0 a nearby fiber admits ALE Ricci-flat Kahler metrics in any Kahler class. Moreover, we generalize Kronheimer's results on hyperkahler 4-manifolds, by giving an explicit classificatio…
Method finds approximate Ricci-flat metrics on Calabi-Yau manifolds.
problem Finding analytic Kähler potentials for Calabi-Yau manifolds.
method Numerically calculating Ricci-flat Kähler potentials via machine learning and fitting to Donaldson's Ansatz.
result Simple analytic expressions for approximately Ricci-flat Kähler potentials are found, including explicit dependence on complex structure parameter.
Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for Ricci-flat manifolds, removing the volume growth assumptions in known results.
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.
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.
The article constructs strong Carrollian geometries at infinity for Ricci flat Einstein manifolds.
problem Understanding projective and Carrollian geometries at infinity for Ricci flat Einstein manifolds.
method Developed a new type of Cartan geometry based on non-effective homogeneous models for projective geometry.
result Carrollian geometries are determined by the projective compactification data of Ricci flat Einstein manifolds.
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.
Flat Ricci-flat manifolds with bounded gradient of Green function are flat.
problem Understanding the rigidity of Ricci-flat manifolds with specific curvature decay.
method Analyzing the gradient of the Green function and using curvature decay conditions.
result Flat Ricci-flat manifolds with bounded gradient of Green function are flat.
An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with singularities conjugate to ADE-type is proved. In 1988, Claude Lebrun gave examples of scalar-flat Kähler ALE metrics with negative mass, on the total space of the bundle over . A corollary of this index …