Related papers: H-projectively-equivalent four-dimensional Kahler …

In this paper we study Kaehler manifolds that are strongly not relative to any projective Kaehler manifold, i.e. those Kaehler manifolds that do not share a Kaehler submanifold with any projective Kaehler manifold even when their metric is…

We give a complete list, for $n \leq 6$, of non-isometric $\mathbb{T}^n$-invariant Kaehler-Einstein manifolds immersed in a finite dimensional complex projective space endowed with the Fubini-Study metric. This solves, in the aforementioned…

We classify non-reductive four-dimensional homogeneous conformally Einstein manifolds.

Let (M,J) be a compact complex 2-manifold which which admits a Kaehler metric for which the integral of the scalar curvature is non-negative. Also suppose that M does not admit a Ricci-flat K\"ahler metric. Then if M is blown up at…

It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as…

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of…

In this paper we study smooth complex projective $4$-folds which are topologically equivalent. First we show that Fano fourfolds are never oriented homeomorphic to Ricci-flat projective fourfolds and that Calabi-Yau manifolds and…

We show that the blow-up of a generalized Kahler 4-manifold in a nondegenerate complex point admits a generalized Kahler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a…

We study generalized Kaehler manifolds for which the corresponding complex structures commute and classify completely the compact generalized Kaehler four-manifolds for which the induced complex structures yield opposite orientations.

Let $(M,\omega)$ be a compact K\"ahler manifold with negative holomorphic sectional curvature. It was proved by Wu-Yau and Tosatti-Yang that $M$ is necessarily projective and has ample canonical bundle. In this paper, we show that any…

We study Kahler surfaces with harmonic anti-selfdual Weyl tensor. We provide an explicit local description, which we use to obtain the complete classification in the compact case. We give new examples of extremal Kahler metrics, including…

Using Hultgren's polytope formulation of the existence of coupled K\"ahler-Einstein (cKE) metrics on toric Fano manifolds, we construct explicit higher-dimensional toric Fano manifolds that admit two coupled K\"ahler-Einstein metrics but no…

We develop in detail the theory of c-projective geometry, a natural analogue of projective differential geometry adapted to complex manifolds. We realise it as a type of parabolic geometry and describe the associated Cartan or tractor…

We construct several examples of compactifications of Einstein metrics. We show that the Eguchi--Hanson instanton admits a projective compactification which is non--metric, and that a metric cone over any (pseudo)--Riemannian manifolds…

We study relations between quaternionic Riemannian manifolds admitting different types of symmetries. We show that any hyperKahler manifold admitting hyperKahler potential and triholomorphic action of S^1 can be constructed from another…

In a previous paper, the first two authors classified complete Ricci-flat ALF Riemannian 4-manifolds that are toric and Hermitian, but non-Kaehler. In this article, we consider general Ricci-flat deformations of such spaces, assuming only…

We present a uniform framework generalising and extending the classical theories of projective differential geometry, c-projective geometry, and almost quaternionic geometry. Such geometries, which we call \emph{projective parabolic…

Motivated by a conjecture in [9] we prove that the K\"ahler cone over a regular complete Sasakian manifold is Ricci-flat and projectively induced if and only if it is flat. We also obtain that, up to $\mathcal D_a$-homothetic…

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…

The geometry of the target space of an N=(2,2) supersymmetry sigma-model carries a generalized Kahler structure. There always exists a real function, the generalized Kahler potential K, that encodes all the relevant local differential…