Related papers: All toric Hermitian ALE gravitational instantons

We prove the vanishing of the Dolbeault cohomology groups on Hermitian manifolds with $dd^c$-harmonic K\"ahler form and positive (1,1)-part of the Ricci form of the Bismut connection. This implies the vanishing of the Dolbeault cohomology…

We investigate complete noncompact Ricci-flat manifolds which are not of maximal volume growth. We show that the manifolds with a curvature decay condition and a holonomy decay condition are asymptotic to torus fibrations over ALE spaces.…

We give a complete classification of left invariant para-K\"ahler structures on four-dimensional simply connected Lie groups up to an automorphism. As an application we discuss some curvatures properties of the canonical connection…

This paper provides a classification result for gravitational instantons with cubic volume growth and cyclic fundamental group at infinity. It proves that a complete hyperk\"ahler manifold asymptotic to a circle fibration over the Euclidean…

A Hermitian Einstein-Weyl manifold is a complex manifold admitting a Ricci-flat Kaehler covering W, with the deck transform acting on W by homotheties. If compact, it admits a canonical Vaisman metric, due to Gauduchon. We show that a…

We discuss instantons on noncommutative four-dimensional Euclidean space. In commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the…

We showed that a sequence of ALH*-gravitational instantons from pairs consisting of a weak del Pezzo surface and a smooth anti-canonical divisor towards a large complex structure limit introduced by Collins, Jacobs and the first author…

We study the non Ricci flat gradient steady K\"{a}hler Ricci soliton with non-negative Ricci curvature and weak integrability condition of the scalar curvature $S$, namely $\underline{\lim}_{r\to \infty} r^{-1}\int_{B_r} S=0$, and show that…

We look at genera of even unimodular lattices of rank $12$ over the ring of integers of $\mathbb{Q}(\sqrt{5})$ and of rank $8$ over the ring of integers of $\mathbb{Q}(\sqrt{3})$, using Kneser neighbours to diagonalise spaces of…

A Theorem of Kirichenko states that the torsion 3-form of the characteristic connection of a nearly K\"ahler manifold is parallel. On the other side, any almost hermitian manifold of type $\mathrm{G}_1$ admits a unique connection with…

We present a simple construction of the instantonic type equation over octonions where its similarities and differences with the quaternionic case are very clear. We use the unified language of Clifford Algebra. We argue that our approach…

We introduce a natural definition of the renormalized volume of a 4-dimensional Ricci-flat ALE space. We then prove that the renormalized volume is always less or equal than zero, with equality if and only if the ALE space is isometric to…

We show that a complete gradient Ricci soliton $(M^n,\,g)$ with constant scalar curvature and a non-parallel closed conformal vector field is isometric to either the Euclidean space, or an Euclidean sphere, or negatively Einstein warped…

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…

For each partition of the positive integer $n= \ell +\sum_{j=1}^\ell d_j$, where $\ell\ge 1$ and $d_j \ge 0$ are integers, we construct a continuous $(\ell-1)$-parameter family of explicit complete gradient steady K\"ahler--Ricci solitons…

The Mordell-Weil lattices (MW lattices) associated to rational elliptic surfaces are classified into 74 types. Among them, there are cases in which the MW lattice is none of the weight lattices of simple Lie algebras or direct sums thereof.…

We study the moduli space of self-dual instantons on $\mathbb{C}P^2$. These are described by an ADHM-like construction which allows to compute the Hilbert series of the moduli space. The latter has been found to be blind to certain compact…

We model A_k and D_k asymptotically locally flat gravitational instantons on the moduli spaces of solutions of U(2) Bogomolny equations with prescribed singularities. We study these moduli spaces using Ward correspondence and find their…

We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…

We show that any tangent cone of a singular shrinking K\"ahler-Ricci soliton is a normal affine algebraic variety. Moreover, the regular set of such a tangent cone in the metric sense coincides with the regular set in the algebraic sense.…