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.
Researchers embed gravitational instantons in higher-dimensional spaces.
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 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.
Instantons on ALF spaces constructed from bow data.
Constructs non-abelian G2-instantons on ALC members of B7 family.
New method solves 'googly problem' for Schwarzschild black holes.
We study the integrability of the conformal geodesic flow (also known as the conformal circle flow) on the --invariant gravitational instantons. On a hyper--Kähler four--manifold the conformal geodesic equations reduce to geodesic equations of a charged particle moving in a constant self--dual magnetic field. In…
Paper shows Ricci flow with surgery converging to Taub-NUT metric.
Solves geodesic equations on specific metrics.
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.
Study instanton metrics via Taub-NUT deformations.
Instantons on multi-Taub-NUT spaces are mapped to bow representations.
Researchers found a new 8D Taub-NUT-like metric using harmonic superspace.
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.
Study on asymptotic behavior of Taub-NUT type solitons and construction of new ALF Calabi-Yau metrics.
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.
Ricci flow converges to Taub-NUT metric under specific conditions.
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.
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 …
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.
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 …
The aim of the paper is to determine left-invariant,anti-self-dual, non conformally flat, Riemannian metrics on four-dimensional Lie groups.
Classifies instantons on ALF multi-Taub-NUT spaces and ties them to bow solutions.
Study shows instantons and monopoles 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…
We show the existence of strictly almost-Kahler anti-self-dual metrics on certain 4-manifolds by deforming scalar-flat Kahler metrics. On the other hand, we prove the non-existence of such metrics on certain other 4-manifolds by means of Seiberg-Witten theory. In the process, we provide a simple new proof of the fact t…
Recently, Atiyah and LeBrun proved versions of the Gauss-Bonnet and Hirzebruch signature Theorems for metrics with edge-cone singularities in dimension four, which they applied to obtain an inequality of Hitchin-Thorpe type for Einstein edge-cone metrics. Interestingly, many natural examples of edge-cone metrics in dim…
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.
An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with cyclic quotient singularities is proved. We present two applications of this theorem. The first is to compute the dimension of the deformation space of the Calderbank-Singer scalar-flat Kahler toric ALE spaces. A corollary of t…
We show that any hyperbolic Inoue surface (or Inoue-Hirzebruch surface of even type) admits anti-self-dual bihermitian structures. The same result also holds for any of its small deformations as far as its anti-canonical system is non-empty. Similar results are obtained for parabolic Inoue surfaces. Our method also yie…
In this note we prove that a (anti-)self dual quasi Yamabe soliton with positive sectional curvature is rotationally symmetric. This generalizes a recent result of G. Huang and H. Li in dimension four. Whence, (anti-) self dual gradient Yamabe solitons with positive sectional curvature is rotationally symmetric. We als…
We prove an energy identity for anti-self-dual connections on the product C\timesΣof the complex plane and a Riemann surface. The energy is a multiple of a basic constant that is determined from the values of a corresponding Chern-Simons functional on flat connections and its ambiguity under gauge transformations. For …
Donaldson-Friedman constructed anti-self-dual classes on using twistor space. We show that some of these conformal classes have almost-Kähler representatives.
New extremal Kähler metrics found on 4-manifolds with U(2) symmetry.
New metric found for 4-manifolds with specific properties.
It is known that the almost-Kaehler anti-self-dual metrics on a given 4-manifold sweep out an open subset in the moduli space of anti-self-dual metrics. However, we show here by example that this subset is not generally closed, and so need not sweep out entire connected components in the moduli space. Our construction …
The paper proves properties of Kähler surfaces with zero scalar curvature.
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 …
All anti-self-dual Einstein metrics with non-zero cosmological constant arise from a single second-order PDE.
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.