Related papers: Almost K\"ahler metrics and pp-wave spacetimes

We give an explicit formula for the quaternionic K\"ahler metrics obtained by the HK/QK correspondence. As an application, we give a new proof of the fact that the Ferrara-Sabharwal metric as well as its one-loop deformation is quaternionic…

We prove that a certain class of ALE spaces always has a Kahler conformal compactification, and moreover provide explicit formulas for the conformal factor and the Kahler potential of said compactification. We then apply this to give a new…

A tractable definition of the homogeneous nearly K\"ahler structure on $\mathbb{C}P^3$ is given via the Hopf fibration, facilitating explicit computations and analysis. The description extends to all homogeneous metrics on $\mathbb{C}P^3$,…

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 formulate a correspondence between affine and projective special K\"ahler manifolds of the same dimension. As an application, we show that, under this correspondence, the affine special K\"ahler manifolds in the image of the rigid r-map…

In this paper we deal with quadratic metric-affine gravity, which we briefly introduce, explain and give historical and physical reasons for using this particular theory of gravity. Further, we introduce a generalisation of well known…

The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metric. It is shown that generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized…

We consider holography of two pp-wave metrics in conformal gravity, their one point functions, and asymptotic symmetries. One of the metrics is a generalization of the standard pp-waves in Einstein gravity to conformal gravity. The…

We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic,…

Given a path of almost-K\"ahler metrics compatible with a fixed symplectic form on a compact 4-manifold such that at time zero the almost-K\"ahler metric is an extremal K\"ahler one, we prove, for a short time and under a certain…

We prove that the Penrose limit of a Lorentzian metric along an affinely parametrized null geodesic is intrinsic, but intrinsic on a weighted associated-graded model determined by the null filtration rather than on a canonically identified…

Consider a divisor D with simple normal crossings in a compact K\"ahler manifold X. We show in this article that a K\"ahler metric in an arbitrary class, with constant scalar curvature and cusp singularities along the divisor is unique in…

We study Lorentzian manifolds $(M, g)$ of dimension $n\geq 4$, equipped with a maximally twisting shearfree null vector field $p_o$, for which the leaf space $S = M/\{\exp t p_o\}$ is a smooth manifold. If $n = 2k$, the quotient $S =…

We classify flat strict nearly K\"ahler manifolds with (necessarily) indefinite metric. Any such manifold is locally the product of a flat pseudo-K\"ahler factor of maximal dimension and a strict flat nearly K\"ahler manifold of split…

We propose a formulation of the Penrose plane wave limit in terms of null Fermi coordinates. This provides a physically intuitive (Fermi coordinates are direct measures of geodesic distance in space-time) and manifestly covariant…

We study the space of nearly K\"{a}hler structures on compact 6-dimensional manifolds. In particular, we prove that the space of infinitesimal deformations of a strictly nearly K\"{a}hler structure (with scalar curvature scal) modulo the…

We provide an explicit formula for the Fefferman-Graham-ambient metric of an $n$-dimensional conformal $pp$-wave in those cases where it exists. In even dimensions we calculate the obstruction explicitly. Furthermore, we describe all…

In this paper we provide new necessary and sufficient conditions for the existence of K\"ahler-Einstein metrics on small deformations of a Fano K\"ahler-Einstein manifold. We also show that the Weil-Petersson metric can be approximated by…

In this paper, we construct metallic K\"ahler and nearly metallic K\"ahler structures on Riemanian manifolds. For such manifolds with these structures, we study curvature properties. Also we describe linear connections on the manifold,…

We use Penrose limits to approximate quasinormal modes with large real frequencies. The Penrose limit associates a plane wave to a region of spacetime near a null geodesic. This plane wave can be argued to geometrically realize the…