Related papers: Gravitational instantons admit hyper-K\"ahler stru…

We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points…

In this paper we introduce the twistor space of a Riemannian manifold with an even Clifford structure. This notion generalizes the twistor space of quaternion-Hermitian manifolds and weak-Spin(9) structures. We also construct almost complex…

We develop a global twistor correspondence for pseudo-Riemannian conformal structures of signature (++--) with self-dual Weyl curvature. Near the conformal class of the standard indefinite product metric on S^2 x S^2, there is an…

We investigate the integrability of almost complex structures on the twistor space of an almost quaternionic manifold constructed with the help of a quaternionic connection. We show that if there is an integrable structure it is independent…

We give a simple and uniform construction of essentially all known deformation classes of gravitational instantons with ALF, ALG or ALH asymptotics and nonzero injectivity radius. We also construct new ALH Ricci flat metrics asymptotic to…

We complete the classification of six-dimensional strongly unimodular almost nilpotent Lie algebras admitting complex structures. For several cases we describe the space of complex structures up to isomorphism. As a consequence we determine…

We derive an explicit formula for the ADM mass of asymptotically locally Euclidean (ALE) almost K\"ahler manifolds. The formula expresses the mass in terms of the total Hermitian scalar curvature and topological data associated with the…

We study the geometric properties of a $2m$-dimensional complex manifold $\mathcal{M}$ admitting a holomorphic reduction of the frame bundle to the structure group $P \subset \mathrm{Spin}(2m,\mathbb{C})$, the stabiliser of the line spanned…

It is well-known that topological sigma-models in 2 dimensions constitute a path-integral approach to the study of holomorphic maps from a Riemann surface S to an almost complex manifold K, the most interesting case being that where K is a…

We investigate T-duality transformation on an almost bi-hermitian space with torsion. By virtue of the Buscher rule, we completely describe not only the covariant derivative of geometrical objects but also the Nijenhuis tensor. We apply…

We study the integrability to second order of infinitesimal Einstein deformations on compact Riemannian and in particular on K\"ahler manifolds. We find a new way of expressing the necessary and sufficient condition for integrability to…

For an almost contact metric manifold $N$, we find conditions for which either the total space of an $S^1$-bundle over $N$ or the Riemannian cone over $N$ admits a strong K\"ahler with torsion (SKT) structure. In this way we construct new…

The monopole equations in the dual abelian theory of the N=2 gauge-theory, recently proposed by Witten as a new tool to study topological invariants, are shown to be the simplest elements in a class of instanton equations that follow from…

We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special K\"ahler holonomy. Motivated by certain curvature…

In this paper we study invariant almost Hermitian geometry on generalized flag manifolds which the isotropy representation decompose into two or three irreducible components. We will provide a classification of such flag manifolds admitting…

We introduce the notion of even Clifford structures on Riemannian manifolds, a framework generalizing almost Hermitian and quaternion-Hermitian geometries. We give the complete classification of manifolds carrying parallel even Clifford…

We study compact almost complex manifolds admitting a Hermitian metric satisfying an integral condition involving $\overline \partial$-harmonic $(0,1)$-forms. We prove that this integral condition is automatically satisfied, if the…

In this paper, we demonstrate that on an almost Hermitian manifold $(M^{2n}, J, ds^2)$, a 2-form $\varphi=S^*\Phi$, the pulling back of the K\"ahler form $\Phi$ on the twistor bundle over $M^{2n}$, is non-degenerate if the squared norm…

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…

We give a complete classification of supersymmetric gravitational instantons in Euclidean N=2 supergravity coupled to vector multiplets. An interesting class of solutions is found which corresponds to the Euclidean analogue of stationary…