Related papers: Twistor and Reflector Spaces of Almost Para-Quater…

By generalizing and extending some of the earlier results derived by Manin and Merkulov, a twistor description is given of four-dimensional N-extended (gauged) self-dual supergravity with and without cosmological constant. Starting from the…

The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact $4$-dimensional solvmanifolds without any integrable almost complex structure. According to the classification…

If $W_+$ denotes the self dual part of the Weyl tensor of any K\"ahler 4-manifold and $S$ its scalar curvature, then the relation $|W_+|^2 = S^2/6$ is well-known. For any almost K\"ahler 4-manifold with $S \ge 0$, this condition forces the…

In contrast to the classical twistor spaces whose fibres are 2-spheres, we introduce twistor spaces over manifolds with almost quaternionic structures of the second kind in the sense of P. Libermann whose fibres are hyperbolic planes. We…

We classify the holomorphic structures of the tangent vertical bundle T of the twistor fibration of a quaternionic manifold (M,Q) of dimension bigger than four. In particular, we show that any self-dual quaternionic connection on (M, Q)…

We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with vanishing first Betti number, we express…

Let Z be a compact complex (2n+1)-manifold which carries a {\em complex contact structure}, meaning a codimension-1 holomorphic sub-bundle D of TZ which is maximally non-integrable. If Z admits a K\"ahler-Einstein metric of positive scalar…

We characterise, in the setting of the Kodaira-Spencer deformation theory, the twistor spaces of (co-)CR quaternionic manifolds. As an application, we prove that, locally, the leaf space of any nowhere zero quaternionic vector field on a…

We consider a four dimensional Riemannian manifold M with a metric g and affinor structure q. The local coordinates of these tensors are circulant matrices. Their first orders are (A, B, C, B), A, B, C\in FM and (0, 1, 0, 0), respectively.…

In this paper a bijective correspondence between superminimal surfaces of an oriented Riemannian $4$-manifold and particular Lagrangian submanifolds of the twistor space over the $4$-manifold is proven. More explicitly, for every…

For any 4D split-signature conformal structure, there is an induced twistor distribution on the 5D space of all self-dual totally null 2-planes, which is $(2,3,5)$ when the conformal structure is not anti-self-dual. Several examples where…

We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kaehler--Weyl structure. We then use analytic continuation to pass from the para-complex to the complex setting and thereby show any…

In this paper we review some results on the Riemannian and almost Hermitian geometry of twistor spaces of oriented Riemannian $4$-manifolds with emphasis on their curvature properties.

We show that a compact oriented riemannian four-manifold with harmonic and pinched self-dual Weyl curvature is anti-self-dual if the type is nonpositive. The main part is to show that there is an almost-K\"ahler structure outside the zero…

Vasiliev equations facilitate globally defined formulations of higher-spin gravity in various correspondence spaces associated with different phases of the theory. In the four-dimensional case this induces a map from a generally covariant…

We prove that compact quaternionic-K\"ahler manifolds of positive scalar curvature admit no almost complex structure, even in the weak sense, except for the complex Grassmannians $Gr_2(C^{n+2})$. We also prove that irreducible inner…

The space ${\mathcal A}$ of almost complex structures on a closed manifold $M$ is studied. A natural parametrization of the space ${\mathcal A}$ is defined. It is shown, that ${\mathcal A}$ is a infinite dimensional complex weak…

Let $X$ be a quasi-projective curve, compactified to $(Y,D)$ with $X=Y-D$. We construct a Deligne-Hitchin twistor space out of moduli spaces of framed $\lambda$-connections of rank $2$ over $Y$ with logarithmic singularities and…

The twistor space of the moduli space of solutions of Hitchin's self-duality equations can be identified with the Deligne-Hitchin moduli space of $\lambda$-connections. We use real projective structures on Riemann surfaces to prove the…

We find necessary and sufficient conditions for a Riemannian four-dimensional manifold $(M, g)$ with anti-self-dual Weyl tensor to be locally conformal to a Ricci--flat manifold. These conditions are expressed as the vanishing of scalar and…