Related papers: Twistor Forms on Kaehler Manifolds

The twistor construction is applied for obtaining examples of generalized complex structures (in the sense of N. Hitchin) that are not induced by a complex or a symplectic structure.

Tractors and Twistors bundles both provide natural conformally covariant calculi on $4D$-Riemannian manifolds. They have different origins but are closely related, and usually constructed bottom-up through prolongation of defining…

In this paper, we characterize Riemannian 4-manifold in terms of its almost Hermitian twistor spaces $(Z,g_t,\mathbb{J}_{\pm})$. Some special metric conditions (including Balanced metric condition, first Gauduchon metric condition) on…

In this paper, we construct tools from the holomorphic twistor spaces that we introduced in \cite{Gindi1} to derive results about the complex geometries of their base manifolds. In particular, we develop a new approach to studying…

We study Riemannian foliations with complex leaves on Kaehler manifolds. The tensor T, the obstruction to the foliation be totally geodesic, is interpreted as a holomorphic section of a certain vector bundle. This enables us to give…

We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.

We determine the twistor deformation of rank one local systems on compact Kaehler manifolds which correspond to smooth twistor modules of rank one in the sense of C. Sabbah. Our proof is rather elementary, and uses a natural description of…

In this work a proposal for definition of twistors on generic curved spaces is exposed and investigated. We consider superpositions of nearly autoparallel and nearly geodesic maps (nearly conformal maps, nc-maps) of (pseudo-)Riemannian…

We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors…

The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity…

Twistor correspondences for R-invariant indefinite self-dual conformal structures on R^4 are established explicitly. These correspondences are written down by using a natural integral transform from functions on a two dimensional cylinder…

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the…

This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a…

We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the…

We introduce in this paper normal twistor equations for differential forms and study their solutions, the so-called normal conformal Killing forms. The twistor equations arise naturally from the canonical normal Cartan connection of…

Generalization of twistor spinors to K\"ahler manifolds which are called K\"ahlerian twistor spinors are considered. We find the differential equation satisfied by the bilinear forms of K\"ahlerian twistor spinors. We show that the bilinear…

In this manuscript we study natural symmetries of Kaehler manifolds: constant holomorphic sectional curvature Kaheler manifolds, semisymmetric Kaehler manifolds and holomorphically pseudosymmetric Kaehler manifolds. We get characterization…

A theorem of Kuranishi tells us that the moduli space of complex structures on any smooth compact manifold is always locally a finite-dimensional space. Globally, however, this is simply not true; we display examples in which the moduli…

A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the…

We complete the classification of all smooth 4-dimensional Kahler geometries admitting a twistor (conformal Killing-Yano) 2-form invariant under a 2-torus action. We establish that there are six geometrically distinct families, and we…