Related papers: On 2-dimensional Kaehler metrics with one holomorp…
We prove that there are just two types of isolated singularities of special K\"ahler metrics in real dimension two provided the associated holomorphic cubic form does not have essential singularities. We also construct examples of such…
We study general linear perturbations of a class of 4d real-dimensional hyperkahler manifolds obtainable by the (generalized) Legendre transform method. Using twistor methods, we show that deformations can be encoded in a set of holomorphic…
A construction of Kaehler-Einstein metrics using Galois coverings, studied by Arezzo-Ghigi-Pirola, is generalized to orbifolds. By applying it to certain orbifold covers of P^n which are trivial set theoretically, one obtains new Einstein…
We use twistor methods to promote Namikawa's universal Poisson deformations of conic affine symplectic singularities to families of hyperk\"ahler structures deforming hyperk\"ahler cone metrics. The metrics we produce are generally…
Motivated in part by the bi-gravity approach to massive gravity, we introduce and study the multimetric Finsler geometry. For the case of an arbitrary number of dimensions, we study some general properties of the geometry in terms of its…
We study off-shell rigid limits for the kinetic and scalar-potential terms os a single N=2 hypermultiplet. In the kinetic term, these rigid limits establish relations between four-dimensional quaternion-Kahler and hyper-Kahler target spaces…
The metric to the two-dimensional dilaton gravity can be writen in an alternative form, similar to the two-dimensional Schwarzschild metric, and allow us the identification of some quantitiies with those equivalent in the Schwarzschild…
A Hermitian metric on a complex manifold of complex dimension $n$ is called {\em astheno-K\"ahler} if its fundamental $2$-form $F$ satisfies the condition $\partial \overline \partial F^{n - 2} =0$. If $n =3$, then the metric is {\em strong…
Four dimensional simply connected Lie groups admitting a pseudo K\"ahler metric are determined. The corresponding Lie algebras are modelized and the compatible pairs $(J,\omega)$ are parametrized up to complex isomorphism (where $J$ is a…
We construct all complete metrics of cohomogeneity one G(2) holonomy with S^3 x S^3 principal orbits from gauged supergravity. Our approach rests on a generalization of the twisting procedure used in this framework. It corresponds to a…
We study the construction and classification of weakly Bochner-flat (WBF) metrics (i.e., Kahler metrics with coclosed Bochner tensor) on compact complex manifolds. A Kahler metric is WBF if and only if its `normalized' Ricci form is a…
Given a semi-Riemannian $4$-manifold $(M,g)$ with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of K\"ahler metrics $g_K$ is constructed, defined on an…
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…
We prove that every Kaehler metric, whose potential is a function of the time-like distance in the flat Kaehler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local…
We derive a local ansatz for generalized K\"ahler surfaces with nondegenerate Poisson structure and a biholomorphic $S^1$ action which generalizes the classic Gibbons-Hawking ansatz for invariant hyperK\"ahler manifolds, and allows for the…
For a compact relative K\"ahler fibration over a compact K\"ahler manifold with negative holomorphic sectional curvature, if the relative K\"ahler form on each fiber also exhibits negative holomorphic sectional curvature, we can construct…
We review the relation between 4n-dimensional quaternion-Kahler metrics with n+1 abelian isometries and superconformal theories of n+1 tensor supermultiplets. As an application we construct the class of eight-dimensional quaternion-Kahler…
The group SU(2)*SU(2) acts naturally on SL(2,C) by simultaneous right and left multiplication. We study the Kahler metrics invariant under this action using global Kahler potentials. The volume growth and various curvature quantities are…
A holomorphy potential is a complex valued function whose complex gradient, with respect to some K\"ahler metric, is a holomorphic vector field. Given $k$ holomorphic vector fields on a compact complex manifold, form, for a given K\"ahler…
We study holomorphic 2-forms on projective (or compact Kaehler) threefolds not of general type and prove that in almost all cases the 2-form is created by some standard process. This means roughly that every 2-form is induced by a…