Related papers: Conformally K\"ahler, Einstein-Maxwell metrics on …
In this note we use the Calabi ansatz, in the context of metrics with conical singularities along a divisor, to produce regular Calabi-Yau cones and K\"ahler-Einstein metrics of negative Ricci with a cuspidal point. As an application, we…
We point out how some recent developments in the theory of constant scalar curvature K\"ahler metrics can be used to clarify the existence issue for such metrics in the special case of geometrically ruled complex surfaces.
A new construction is presented of scalar-flat Kaehler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable…
This is an expository article, closely following the author's lecture at the 2014 Journal Differential Geometry conference.
For any elliptic K3 surface $\mathfrak{F}: \mathcal{K} \rightarrow \mathbb{P}^1$, we construct a family of collapsing Ricci-flat K\"ahler metrics such that curvatures are uniformly bounded away from singular fibers, and which…
Conditions for the existence of K\"ahler-Einstein metrics and central K\"ahler metrics [MS] along with examples, both old and new, are given on classes of Lorentzian $4$-manifolds with two distinguished vector fields. The results utilize…
In this article, I prove the following statement: Every compact complex surface with even first Betti number is deformation equivalent to one which admits an extremal K\"ahler metric. In fact, this extremal K\"ahler metric can even be taken…
We show that if a compact K\"ahler manifold admits a weighted extremal metric for the action of a torus, so too does its blowup at a relatively stable point that is fixed by both the torus action and the extremal field. This generalises…
We prove the lower semi-continuity of the coercivity threshold of Mabuchi functional along a degenerate family of normal compact K\"ahler varieties with klt singularities. Moreover, we establish the existence of singular cscK metrics on…
In this article, we construct explicit analytical exact solutions to the six and higher dimensional Einstein-Maxwell theory. In all solutions, a subspace of the metric is the Eguchi-Hanson space where the metric functions are completely…
In this paper, we found new classes of solutions to the Einstein-Maxwell field equations with matter anisotropic distribution incorporating a particular form of electric field intensity within the framework of general relativity. We use a…
The formulation of the Einstein field equations admitting two Killing vectors in terms of harmonic mappings of Riemannian manifolds is a subject in which Charlie Misner has played a pioneering role. We shall consider the hyperbolic case of…
In this note we present a new proof that Killing horizons are equipotential hypersurfaces for the electric and the magnetic scalar potential, that makes no use of gravitational field equations or the assumption about the existence of…
This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as…
We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If $M$ is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein…
We prove the existence of Kahler-Einstein metrics on a nonsingular section of the Grassmannian $\mathrm{Gr}(2, 5)\subset\mathbb{P}^9$ by a linear subspace of codimension 3, and the Fermat hypersurface of degree 6 in $\mathbb{P}(1,1,1,2,3)$.…
We identify an anisotropic divergence-free conformal Killing tensor $K_{jl}$ for static spherically symmetric spacetimes, and write the conformal Killing gravity equations as Einstein equations augmented by this tensor. The field equations…
We prove the existence of complete cohomogeneity one triaxial K\"ahler-Einstein metrics in dimension four under an action of the Euclidean group $E(2)$. We also demonstrate local existence of Ricci flat K\"ahler metrics of a related type…
We prove that compact K\"ahler manifolds whose sectional curvatures are close to 1/4-pinched have ratios of Chern numbers close to the corresponding ratios of a complex hyperbolic space form. We deduce that the Mostow-Siu surfaces (and…
We show how to write any Kaehler metric of complex dimension 2 admitting a holomorphic isometry as a simple 1-real-function deformation of a Gibbons-Hawking metric. Hyper-Kaehler metrics with a tri-holomorphic isometry (Gibbons-Hawking…