Ancient Ricci flow found from Taub-Bolt metric.
problem Existence of ancient Ricci flow solutions.
method Analysis of Ricci flow from Taub-Bolt metric.
result Non-trivial ancient solution to Ricci flow found.
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13 results for “Taub-Bolt”
Paper shows perturbed Taub-Bolt metric becomes singularity under Ricci flow.
problem Analyzing stability of Taub-Bolt metric under Ricci flow.
method Box argument and construction of Ricci flows on compact manifolds.
result Compact perturbation of Taub-Bolt metric evolves into finite time singularity.
This paper studies the space of harmonic forms and harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find a 2-parameter family of zero mod…
We show that the Riemannian Schwarzschild and the ``Taub-bolt'' instanton solutions are the only spaces (M,g) such that 1) M is a 4-dimensional, simply connected manifold with a Riemannian, Ricci-flat C^2-metric g which admits (at least) a 1-parameter group of isometries H without isolated fixed points on M. 2) The quo…
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.
Einstein manifolds are rigid under certain metric deformations.
problem Characterizing Einstein manifolds that resist volume-preserving metric deformations.
method Various characterizations and constructions of mass-decreasing perturbations.
result Constructs mass-decreasing perturbations of specific metrics.
Study on mode stability of gravitational instantons of type D.
problem Proving mode stability of gravitational instantons of type D.
method Analogous to Lorentzian case, analyze Weyl curvature scalars satisfying a separable Teukolsky equation.
result Prove mode stability, showing no solutions compatible with regularity and asymptotic flatness.
We construct new complete, compact, inhomogeneous Einstein metrics on S^{m+2} sphere bundles over 2n-dimensional Einstein-Kahler spaces K_{2n}, for all n \ge 1 and all m \ge 1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of S^m with S^2 bundles over K_{2n}, for m>1. Additionally,…
Proves uniqueness of certain -symmetric gravitational instantons.
problem Proving uniqueness of -symmetric gravitational instantons.
method Using a divergence identity and results from the -signature theorem.
result Proof of the -symmetric Euclidean Black Hole Uniqueness conjecture.
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.
Study classifies gravitational instantons based on their asymptotic geometry.
problem Classifying gravitational instantons based on their asymptotic properties.
method Investigation of asymptotic geometry of Hermitian non-Kähler Ricci-flat metrics.
result All Hermitian non-Kähler gravitational instantons can be compactified to log del Pezzo surfaces.
This work shows all conformally Kähler, Ricci-flat toric metrics on non-compact surfaces are known families.
problem Characterize all conformally Kähler, Ricci-flat toric metrics on non-compact surfaces.
method Unified construction using axi-symmetric harmonic functions and methods from scalar-flat Kähler metrics.
result All such metrics are ALF and belong to known families.
The study classifies Einstein metrics on a specific total space, revealing various behaviors and transitions.
problem Classifying conformally Kähler, -invariant, Einstein metrics.
method Drawing on Derdziński's results from the 80s, the study classifies metrics on for all .
result The study discovers infinitely many 1-parameter families of Einstein metrics with different behaviors, including asymptotically hyperbolic, ALF, and cone angle limits.