Related papers: Twistor geometry and warped product orthogonal com…

Let $\widetilde{\cal J}(S^{2n})$ be the set of orthogonal complex structures on $TS^{2n}$. We show that the twistor space $\widetilde{\cal J}(S^{2n})$ is a Kaehler manifold. Then we show that an orthogonal almost complex structure $J_f$ on…

We give a new proof that the sphere S^6 does not admit an integrable orthogonal complex structure, as in \cite{LeBrun}, following the methods from twistor theory. We present the twistor space of a pseudo-sphere…

In this paper, we use Clifford algebra and the spinor calculus to study the complex structures on Euclidean space $R^8$ and the spheres $S^4,S^6$. By the spin representation of $G(2,8)\subset Spin(8)$ we show that the Grassmann manifold…

For $n \geq 1$, the twistor space $\mathfrak{Z}(\mathbb{S}^{2n})$ of the conformal $2n$-sphere is biholomorphic to the Zariski closure, taken in the complex Grassmannian manifold $\mathbf{G}(n+1, 2n+2)$, of the set of graphs of…

We consider some classical fibre bundles furnished with almost complex structures of twistor type, deduce their integrability in some cases and study \textit{self-holomorphic} sections of a \textit{symplectic} twistor space. With these we…

This paper resolves a long-standing open problem by providing a classification of Willmore $2$-spheres in $S^n$. We show that any such $2$-sphere is either totally isotropic--originating from the projection of a special twistor curve in the…

This article is a contribution to the understanding of the geometry of the twistor space of a symplectic manifold. We consider the bundle $Z$ with fibre the Siegel domain Sp(2n,R)/U(n) existing over any given symplectic 2n-manifold M. Then,…

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…

In this paper, we demonstrate that on an almost Hermitian manifold $(M^{2n}, J, ds^2)$, a 2-form $\varphi=S^*\Phi$, the pulling back of the K\"ahler form $\Phi$ on the twistor bundle over $M^{2n}$, is non-degenerate if the squared norm…

As in the case of irreducible holomorphic symplectic manifolds, the period domain $Compl$ of compact complex tori of even dimension $2n$ contains twistor lines. These are special $2$-spheres parametrizing complex tori whose complex…

A C-symplectic structure is a complex-valued 2-form which is holomorphically symplectic for an appropriate complex structure. We prove an analogue of Moser's isotopy theorem for families of C-symplectic structures and list several…

We describe complex twistor spaces over inner 3-symmetric spaces $G/H$, such that $H$ acts transitively on the fibre. Like in the symmetric case, these are flag manifolds $G/K$ where $K$ is the centralizer of a torus in $G$. Moreover, they…

A hyperk\"ahler manifold $M$ has a family of induced complex structures indexed by a two-dimensional sphere $S^2 \cong \mathbb{CP}^1$. The twistor space of $M$ is a complex manifold $Tw(M)$ together with a natural holomorphic projection…

The topology of the smooth moduli space of stable rank 2 bundles over a Riemann surface of genus 3 is related to that of the real Grassmannian Gr_4(R^8).

We study the complexity of horizontality in the twistor space $\hat{E}$ associated with an oriented vector bundle $E$ of rank $4$ with a positive-definite metric over a torus. If the horizontality has finite complexity of degree $d>2$ for…

We explicitly describe all SO(7)-invariant almost quaternion-Hermitian structures on the twistor space of the six sphere and determine the types of their intrinsic torsion.

The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate…

In this document we present a twistor correspondence for half-flat almost-Grassmannian structures on real and complex manifolds. We provide foundational results regarding local theory in the complex setting and a global correspondence when…

Let (M,g) be a Riemannian 4-manifold. The twistor space Z->M is a CP1-bundle whose total space Z admits a natural metric h. The aim of this article is to study properties of complex structures on (Z,h) which are compatible with the…

We consider certain fiber bundles over a paraquaternionic contact manifolds, called twistor and reflector spaces, and show that these carry an intrinsic geometric structure that is always integrable.