Paper shows Ricci flow with surgery converging to Taub-NUT metric.
problem Existence of Ricci flow with surgery and topology change.
method Ricci flow with surgery and local topology change.
result Flow converges to Taub-NUT metric on \mathbb{R}^4.
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48 results for “Taub-Nut”
Solves geodesic equations on specific metrics.
problem Explicit geodesic solutions for certain metrics are not known.
method Solves geodesic equations under different constant conditions.
result Explicit solutions not available for all conditions.
We propose a construction of Skyrme fields from holonomy of the spin connection of gravitational instantons. The procedure is implemented for Atiyah-Hitchin and Taub-NUT instantons. The skyrmion resulting from the Taub-NUT is given explicitly on the space of orbits of a left translation inside the whole isometry group.…
The paper explores Kähler structures of Taub-NUT and Kerr spaces.
problem Understanding Kähler properties of gravitational instantons and black holes.
method Analyzing Euclidean Taub-NUT and Kerr metrics using alternative coframes and conformal scaling.
result Euclidean Taub-NUT and Kerr metrics exhibit hyper-Kähler and globally conformally Kähler properties, respectively.
Study instanton metrics via Taub-NUT deformations.
problem Understanding deformations of instanton metrics.
method Using generalized Legendre transform on bow varieties.
result Found Kähler potential on instanton moduli spaces.
Instantons on multi-Taub-NUT spaces are mapped to bow representations.
problem Mapping instantons to bow representations for multi-Taub-NUT spaces.
method Proving gauge equivalence classes correspondence and isometry of moduli spaces.
result Instantons on multi-Taub-NUT spaces are isometric to bow representations.
Researchers found a new 8D Taub-NUT-like metric using harmonic superspace.
problem Finding a new 8-dimensional Taub-NUT-like manifold.
method Used harmonic superspace formalism to derive the metric.
result Derived a new 8D Taub-NUT-like metric.
We study the one-parameter family of twisted Kahler Taub-NUT metrics (discovered by Donaldson), along with two exceptional Taub-NUT-like instantons, and understand them to the extend that should be sufficient for blow-up and gluing arguments. In particular we parametrize their geodesics from the origin, determine curva…
Gravitational instantons are constructed as superpositions of Atiyah-Hitchin and Taub-NUT geometries.
problem Constructing gravitational instantons from Atiyah-Hitchin and Taub-NUT geometries.
method A gluing construction that captures the superposition of moduli spaces of centred SU(2) monopoles and Taub-NUT manifolds.
result Gravitational instantons are explicitly shown to be superpositions of Atiyah-Hitchin and Taub-NUT geometries.
Study on asymptotic behavior of Taub-NUT type solitons and construction of new ALF Calabi-Yau metrics.
problem Asymptotic behavior of steady gradient Kähler-Ricci solitons of Taub-NUT type.
method Determination of asymptotic cone, special case analysis, and construction of new metrics using Tian-Yau-Hein method.
result Construction of new ALF Calabi-Yau metrics on quotients of the Taub-NUT type soliton.
We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series of papers proving the completeness of the bow construction of instantons on mult…
We present a construction of self-dual Yang-Mills connections on the Taub-NUT space. We illustrate it by finding explicit expressions for all SU(2) instantons of instanton number one and generic monodromy at infinity.
We study the Hessian geometry of toric multi-Taub-NUT metrics and their phase change phenomena via the images of their moment maps. This generalizes an earlier paper on toric Gibbons-Hawking metrics.
We introduce a generalization of Taub-NUT deformations for large families of hyper-Kaehler quotients including toric hyper-Kaehler manifolds and quiver varieties, and apply them to the case of the Hilbert schemes of k points on C^2.
Ricci flow converges to Taub-NUT metric under specific conditions.
problem Analyzing convergence of Ricci flow solutions to Taub-NUT metric.
method Study of Ricci flow starting from a specific metric on .
result Ricci flow converges to Taub-NUT metric in infinite time under certain conditions.
The common assertion that the Ricci flows of Einstein spaces with cosmological constant can be modelled by certain classes of nonholonomic frame, metric and linear connection deformations resulting in nonhomogeneous Einstein spaces is examined in the light of the role played by topological three dimensional (3D) Taub-N…
Explicit construction of the basic SU(2) anti-instantons over the multi-Taub--NUT geometry via the classical conformal rescaling method is exhibited. These anti-instantons satisfiy the so-called weak holonomy condition at infinity with respect to the trivial flat connection and decay rapidly. The resulting unital energ…
We construct a family of Calabi-Yau metrics on $\C^3$ with properties analogous to the Taub-NUT metric on $\C^2$, and construct a family of Calabi-Yau 3-fold metric models on the positive and negative vertices of SYZ fibrations with properties analogous to the Ooguri-Vafa metric.
We find sufficient conditions for the absence of harmonic spinors on spin manifolds constructed as cone bundles over a compact Kähler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of…
Complete Calabi-Yau metrics on C^{N+1} are constructed.
problem Constructing complete Calabi-Yau metrics on C^{N+1} for N >= 3.
method Generalized Gibbons-Hawking ansatz with gluing procedure to overcome volume-form defects.
result Calabi-Yau metrics with tangent cone R^N are constructed.
Classifies instantons on ALF multi-Taub-NUT spaces and ties them to bow solutions.
problem Classifying instantons on specific spaces.
method Uses Nahm's equations and bow solutions to construct instantons.
result Constructs holomorphic instanton bundles on multi-Taub-NUT spaces.
Study shows instantons and monopoles decompose into U(1) components.
problem Understanding the asymptotic structure of instantons and monopoles.
method Analysis of multi-centered Taub-NUT manifolds, calorons, and monopoles on R^3.
result Instantons and monopoles asymptotically decompose into U(1) components.
This paper provides a classification result for gravitational instantons with cubic volume growth and cyclic fundamental group at infinity. It proves that a complete hyperkähler manifold asymptotic to a circle fibration over the Euclidean three-space is either the standard $\rl^3 \times \sph^1$ or a multi-Taub-NUT mani…
New extremal Kähler metrics found on 4-manifolds with U(2) symmetry.
problem Finding new extremal Kähler metrics on 4-manifolds with U(2) symmetry.
method Analyzing -invariant metrics, showing they are conformal to two separate Kähler metrics, leading to ambiKähler structures.
result New complete extremal Kähler metrics found on specific 4-manifolds.
The paper proves properties of Kähler surfaces with zero scalar curvature.
problem Characterizing Kähler surfaces with zero scalar curvature.
method Analyzing families of generalized Taub-Nut Kähler surfaces and Burn's metric.
result Proves that certain Kähler surfaces are QCH and of specific types.
We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton. W…
In this paper we exhibit a one-parameter family of new Taub-NUT instantons parameterized by a half-line. The endpoint of the half-line will be the reducible Yang-Mills instanton corresponding to the Eguchi-Hanson-Gibbons L^2 harmonic 2-form, while at an inner point we recover the Pope-Yuille instanton constructed as a …
Special Lagrangian submanifolds emerge from K3 surface collapse.
problem Understanding special Lagrangian submanifolds in K3 surface collapse.
method Lifting affine lines to degenerating sequences of special Lagrangian submanifolds.
result Constructing special Lagrangian two-spheres connecting Taub-NUT bubbles.
In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some conceptual issues on spacetimes provided with generic off-diagonal metrics and ass…
New methods compute geometry of hyperKähler metrics at infinity.
problem Understanding the geometry of hyperKähler metrics at infinity.
method Quasi-asymptotically conical metrics, Taub-NUT deformations, compactification by manifolds with corners.
result Identifies unique tangent cones and cohomology groups.
The paper extends Hawking--Page solutions to various spacetimes with singularities.
problem Understanding the extensions of Hawking--Page solutions with different types of singularities.
method Kaluza--Klein reduction and Christodoulou's methods.
result Extensions of Lorentzian Hawking--Page solutions with null, spacelike singularities, and Cauchy horizons of Taub--NUT type are proven.
Constructs an asymptotic metric for moduli space of centred hyperbolic monopoles.
problem Analyzing the moduli space of centred hyperbolic monopoles.
method Point particle approximation and geodesic motion analysis.
result Obtains a hyperbolic analogue of negative mass Taub-NUT metric.
The paper constructs ALF Calabi-Yau metrics on specific manifolds.
problem Creating higher-dimensional ALF Calabi-Yau metrics.
method Using Taub-NUT deformation of hyperkähler cones and crepant resolutions.
result Existence of ALF Calabi-Yau metrics on certain manifolds.
By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.
Construction of gravitational instantons with non-maximal volume growth via codimension-1 collapsemath.DG
The paper constructs gravitational instantons with unique collapse patterns.
problem Creating gravitational instantons with specific geometric properties.
method Using gluing construction, the metric collapses to quotients of R^3 with specific patterns.
result The constructed gravitational instantons have unique collapse patterns and exceptional points.
We show how the index formula for manifolds with fibered boundaries can be used to compute the index of the Dirac operator on Taub-NUT space twisted by an anti-self-dual generic instanton connection.
In this paper we examine a new class of five dimensional (5D) exact solutions in extra dimension gravity possessing Lie algebroid symmetry. The constructions provide a motivation for the theory of Clifford nonholonomic algebroids elaborated in Ref. hep-th/0501217. Such Einstein-Dirac spacetimes are parametrized by gene…
New method solves 'googly problem' for Schwarzschild black holes.
problem Solving the 'googly problem' for non-chiral field configurations.
method Using twistor space and holomorphic loci to construct a non-self-dual, four-dimensional Kähler metric.
result First instance of a non-self-dual Einstein metric from holomorphic data in twistor space.
Study finds all hyper-Kähler 4-manifolds with specific symmetries and structures.
problem Characterizing hyper-Kähler 4-manifolds with conformal Kähler structures.
method Analyzing twistor elementary states and locally flat spaces, showing compatibility and incompatibility of complex structures.
result Only hyper-Kähler 4-metric with a non-constant Killing-Yano tensor is the half-flat Taub-NUT instanton.
Using Hawking Taub-NUT metric on , where is a positive real number and finding a 4-parameter family of Killing vector fields of , we construct a 5-parameter family of Einstein Randers metrics with non-constant flag curvature.
We construct infinitely many new 1-parameter families of simply connected complete noncompact G_2-manifolds with controlled geometry at infinity. The generic member of each family has so-called asymptotically locally conical (ALC) geometry. However, the nature of the asymptotic geometry changes at two special parameter…
Constructs non-abelian G2-instantons on ALC members of B7 family.
problem Constructing non-abelian G2-instantons on ALC members of B7 family.
method Using co-homogeneity one symmetries, classify and describe the solutions as perturbations of abelian instantons.
result Find a one-parameter family of instantons with polynomial decay.
In a recent paper Donaldson explains how to use an older construction of Joyce to obtain four dimensional local models for scalar-flat Kahler metrics with a 2-torus symmetry. Using this idea, he recovers and generalizes the Taub-NUT metric by including it in a new family of complete scalar-flat toric Kahler metrics. In…
A generalisation of the four-dimensional Kerr-de Sitter metrics to include a NUT charge is well known, and is included within a class of metrics obtained by Plebanski. In this paper, we study a related class of Kerr-Taub-NUT-de Sitter metrics in arbitrary dimensions D \ge 6, which contain three non-trivial continuous p…
New minimal 2-spheres found in hyperkähler 4-manifolds, unstable and not holomorphic.
problem Characterizing stable minimal surfaces in hyperkähler 4-manifolds.
method Gluing construction using Scherk and Taub-NUT surfaces, harmonic map parametrization.
result Existence of unstable minimal 2-spheres with degree-1 Gauss lift, not holomorphic.
We exhibit families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding continuous surjective map from the K3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds.
We construct isometric and conformally isometric embeddings of some gravitational instantons in and . In particular we show that the embedding class of the Einstein--Maxwell instanton due to Burns is equal to . For , Eguchi--Hanson and anti-self-dual Taub-NUT we obtain upp…
The abstract discusses conditions for hyperkähler manifolds and Kähler reduction.
problem Conditions for hyperkähler manifolds and Kähler reduction methods.
method Explicit proof and two-stage Kähler reduction process.
result Explicit proof of necessary and sufficient condition for hyperkähler manifolds.