Related papers: All toric Hermitian ALE gravitational instantons
Gravitational instantons of Bianchi type IX space are constructed in Ashtekar's canonical formalism. Instead of solving the self-duality condition, we fully solve the constraint on the ``initial surface'' and ``Hamiltonian equations''. This…
We give a new construction of Ricci-flat self-dual metrics which is a natural extension of the Gibbons--Hawking ansatz. We also give characterisations of both these constructions, and explain how they come from harmonic morphisms.
We study the $\alpha'$ corrections to self-dual gravitational instantons in the context of the four-dimensional Cano--Ruip\'erez action, which can be obtained by the compactification of the Bergshoeff--de Roo heterotic string effective…
We will answer a question raised by Emmanuel Dror Farjoun concerning the existence of torsion-free abelian groups G such that for any ordered pair of pure elements there is a unique automorphism mapping the first element onto the second…
On a given compact complex manifold or orbifold $(M,J)$, we study the existence of Hermitian metrics $\tilde g$ in the conformal classes of K\"ahler metrics on $(M,J)$, such that the Ricci tensor of $\tilde g$ is of type $(1,1)$ with…
Let $G$ be a linear connected non-compact real simple Lie group and let $K\subset G$ be a maximal compact subgroup of $G$. Suppose that the centre of $K$ isomorphic to $\mathbb{S}^1$ so that $G/K$ is a global Hermitian symmetric space. Let…
We study the space of L^2 harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type. These metrics generalize the geometric structures at infinity of several different well-known classes of metrics, including…
We construct an example of Ricci-flat almost-K\"ahler non-K\"ahler structure in four dimensions.
Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat K\"ahler metrics on a minimal K\"ahler surface whose K\"ahler classes stay in a compact…
In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a K\"ahler model. The first theorem could be considered as a rigidity result for the K\"ahler-Ricci soliton structure on $\mathbb{S}^2\times…
We continue our study of the noncommutative algebraic and differential geometry of a particular class of deformations of toric varieties, focusing on aspects pertinent to the construction and enumeration of noncommutative instantons on…
We prove existence, uniqueness and structure results for complete noncompact 7-dimensional G2-holonomy metrics with ALC (asymptotically locally conical) asymptotics. We regard such spaces as G2-analogues of ALF gravitational instantons in…
In this paper, we classify and construct five-dimensional black holes on gravitational instantons in vacuum Einstein gravity, with RxU(1)xU(1) isometry. These black holes have spatial backgrounds which are Ricci-flat gravitational…
We present a novel approach to constructing gravitational instantons based on the observation that the gravitational action of general relativity in its teleparallel formulation can be expressed as a product of the torsion and excitation…
We describe the local structure of self-dual gradient Ricci solitons in neutral signature. If the Ricci soliton is non-isotropic then it is locally conformally flat and locally isometric to a warped product of the form $I\times_\varphi…
The double copy is a map from non-abelian gauge theories to gravity, that has been demonstrated both for scattering amplitudes and exact classical solutions. In this study, we reconsider the double copy for exact solutions that are…
Let $\pi : \mathcal X \to S$ be a local universal family of compact Ricci-flat K\"ahler manifolds over a smooth base $S$. The complexified K\"ahler cones of each fiber of the family form a holomorphic fiber bundle $\mathcal K \to S$. We…
We construct D_k asymptotically locally flat gravitational instantons as moduli spaces of solutions of Nahm equations. This allows us to find their twistor spaces and Kahler potentials.
We prove two rigidity theorems on holomorphic isometries into homogeneous bounded domains. The first shows that a K\"ahler-Ricci soliton induced by the homogeneous metric of a homogeneous bounded domain is trivial, i.e. K\"ahler-Einstein.…
A broad class of higher dimensional instanton solutions are found for a theory which contains gravity, a scalar field and antisymmetric tensor fields of arbitrary rank. The metric used, a warp product of an arbitrary number of any compact…