Related papers: Gravitational instantons admit hyper-K\"ahler stru…
Recently N.Nekrasov and A.Schwarz proposed a modification of the ADHM construction of instantons which produces instantons on a noncommutative deformation of the 4-dimensional real affine space. In this paper we study the relation between…
We consider sphere bundles P and P' of totally null planes of maximal dimension and opposite self-duality over a 4-dimensional manifold equipped with a Weyl or Riemannian geometry. The fibre product PP' of P and P' is found to be…
A $p$-K\"ahler structure on a complex manifold of complex dimension $n$ is given by a $d$-closed transverse real $(p,p)$-form. In the paper we study the existence of $p$-K\"ahler structures on compact quotients of simply connected Lie…
We obtain a correspondence between irreducible real parallel spinors on pseudo-Riemannian manifolds $(M,g)$ of signature $(4,3)$ and solutions of an associated differential system for three-forms that satisfy a homogeneous algebraic…
In the context of 4d effective gravity theories with 8 supersymmetries, we propose to unify, strenghten, and refine the several swampland conjectures into a single statement: the structural criterion, modelled on the structure theorem in…
Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong…
We study almost K\"ahler manifolds whose curvature tensor satisfies the second curvature condition of Gray (shortly ${\cal{AK}}_2$). This condition is interpreted in terms of the first canonical Hermitian connection. It turns out that this…
The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by…
We revisit an emergent gravity scenario in $(4+1)$ dimensions underlying a propagating geometric torsion ${\cal H}_3$ with a renewed interest. We show that a pair-symmetric $4$th order curvature tensor is sourced by a two-form Neveu-Schwarz…
Firstly we give a condition to split off the K"ahler factor from a nearly pseudo-K"ahler manifold and apply this to get a structure result in dimension 8. Secondly we extend the construction of nearly K"ahler manifolds from twistor spaces…
We explore how the topology of spacetime fabric is encoded into the local structure of Riemannian metrics using the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to prove that a…
Explicit formulas for the $G_2$-components of the Riemannian curvature tensor on a manifold with a $G_2$ structure are given in terms of Ricci contractions. We define a conformally invariant Ricci-type tensor that determines the…
We conjecture that any scalar-flat K\"ahler surface in which the Weyl tensor acting on 2-forms annihilates the Ricci form must be either Ricci-flat or locally isometric to a Riemannian product of two real surfaces with mutually opposite…
We investigate four-dimensional, self-dual gravitational instantons endowed with a product structure RxM_3, where M_3 is homogeneous of Bianchi type. We analyze the general conditions under which Euclidean-time evolution in the…
In this note, we revisit some well-known examples of instantons on flat space that were originally discovered in the physics literature. In particular, we explain how the basic instanton on $\mathbb{R}^4$, with its flat hyperkaehler…
There is a sequence of positive numbers $\delta_{2n}$, such that for any connected $2n$-dimensional Riemannian manifold $M$, there are two mutually exclusive possibilities: $1)$ There is a complex structure on $M$ making it into a K\"ahler…
It is considered a differentiable manifold equipped with a pseudo-Riemannian metric and an almost contact 3-struc\-ture so that an almost contact metric structure and two almost contact B-metric structures are generated. There are…
In this expository paper we review some twistor techniques and recall the problem of finding compact differentiable manifolds that can carry both K\"ahler and non-K\"ahler complex structures. Such examples were constructed independently by…
A torsion-free G_2 structure admitting an infinitesimal isometry is shown to give rise to a 4-manifold equipped with a complex symplectic structure and a 1-parameter family of functions and 2-forms linked by second order equations.…
On an oriented, compact, connected, real four-dimensional manifold, $M$, we introduce a topological Lagrangian gauge field theory with a Bogomol'nyi structure that leads to non-singular, finite-Action, stable solutions to the variational…