The study generalizes twistor spinors to Kähler manifolds and finds bilinear form equations.
problem Generalizing twistor spinors to Kähler manifolds.
method Finding differential equations and reducing them to conformal Killing-Yano equations.
result Bilinear forms of Kählerian twistor spinors reduce to Kählerian conformal Killing-Yano equations under certain conditions.
Researchers derive symmetry operators from twistor spinors in curved spacetime.
problem Deriving symmetry operators for gauged twistor spinors in curved backgrounds.
method Using gauged twistor spinors and conformal Killing-Yano forms, symmetry operators are constructed.
result Symmetry operators can be obtained from ordinary twistor spinors in constant curvature backgrounds.
Twistor theory connects space-time to complex curves, solving physics equations.
problem Solving equations in mathematical physics using twistor theory.
method Encoding solutions into twistor cohomology and using twistor correspondences.
result Explicit examples of Yang-Mills and gravitational instantons.
2D twistor manifolds explain Teukolsky equations for rotating black holes.
problem Understanding the geometry of Teukolsky equations for rotating black holes.
method Using 2D twistor manifolds to explain the Teukolsky equations.
result All geometric structures can be understood by considering a 2D twistor manifold.
The paper proves unique properties of Riemannian twistor spaces under specific curvature conditions.
problem Characterizing Riemannian twistor spaces under vanishing curvature conditions.
method Moving frame method, classification, and nonexistence proofs.
result The only twistor space with parallel Bochner tensor is CP3. On a Kähler spin manifold Kählerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the Kähler structure, called Kählerian twistor (Penrose) operator. We study Kählerian twistor spinors a…
Harmonic spinors linked to twistor spinors via potential forms and conformal Killing-Yano forms.
problem Connecting harmonic spinors and twistor spinors using mathematical operators.
method Constructing symmetry operators from conformal Killing-Yano forms and finding transformation operators between twistor and harmonic spinors in terms of potential forms.
result Operators transforming gauged twistor spinors to gauged harmonic spinors and algebraic conditions for Seiberg-Witten equations solutions.
In a recent paper (math.DG/0701278) we constructed a series of new Moishezon twistor spaces which is a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon twistor spaces on nCP^2 for arbitrary n>2, which can be regarded as a generalizati…
Study on the topology of twistor discriminant loci in 4-sphere.
problem Topology of twistor discriminant loci of algebraic surfaces.
method Classical algebraic geometry techniques applied to twistor fibration.
result Real dimension of twistor discriminant locus is always 2 except for two exceptional cases.
In this paper we investigate a family of Moishezon twistor spaces on the connected sum of 4 complex projective planes, which can be regarded as a direct generalization of the twistor spaces on 3CP^2 of double solid type studied by Poon and Kreussler-Kurke. These twistor spaces have a natural structure of double coverin…
Study pseudo-hyperkähler geometry of curves in hyperkähler twistor spaces.
problem Understanding the geometry of rational curves in twistor spaces.
method Investigate pseudo-hyperkähler geometry of higher degree rational curves.
result Characterize the pseudo-hyperkähler structure of rational curves.
The paper examines curvature properties of twistor spaces.
problem None explicitly stated in the abstract.
method Review of Riemannian and almost Hermitian geometry of twistor spaces.
result Curvature properties of twistor spaces are explored.
Study on surfaces in flag threefold with constraints on twistor fibers.
problem Understanding the arrangement and existence of twistor fibers in surfaces of specific bidegree.
method Analyzing surfaces of bidegree (1,d) in the flag threefold, proving existence and non-existence of twistor fibers.
result Existence and non-existence of surfaces containing specific numbers of twistor fibers, with improved results for d=2 and d=3.
Develops twistor theory for foliated manifolds, proving orbifold results.
problem Classical twistor theory applied to foliated manifolds.
method Constructs twistor space of normal bundle, proves foliated versions of results.
result Obtains orbifold versions of classical results.
The paper defines a new twistor space for Riemannian manifolds with even Clifford structures.
problem No specific problem stated; the focus is on a new mathematical structure.
method Introduced a new twistor space for Riemannian manifolds with even Clifford structures.
result Constructed almost complex structures on the twistor space for parallel even Clifford structures and proved integrability in some cases.
In this paper we investigate Moishezon twistor spaces which have a structure of double covering over a very simple rational threefold. These spaces can be regarded as a direct generalization of the twistor spaces studied by Poon and Kreussler-Kurke to the case of arbitrary signature. In particular, the branch divisor o…
The paper embeds CR manifolds into twistor spaces and constructs neutral hyperkähler metrics.
problem Embedding CR manifolds into twistor spaces and constructing neutral hyperkähler metrics.
method Embedding a real analytic twistor CR manifold into the twistor space of a Poincaré-Einstein metric, constructing the associated Fefferman ambient metric as a neutral hyperkähler metric.
result The construction of neutral hyperkähler metrics associated with twistor CR manifolds.
We compute the hessian of the natural Hermitian form successively on the Calabi family of a hyperkähler manifold, on the twistor space of a 4-dimensional anti-self-dual Riemannian manifold and on the twistor space of a quaternionic Kähler manifold. We show a strong convexity property of the cycle space of twistor lines…
Study shows algebraic dimension of certain twistor spaces is limited to 1 or 0.
problem Limiting the algebraic dimension of twistor spaces over n#CP^2.
method Analyzing the fundamental system as a pencil and proving constraints on algebraic dimension.
result Twistor spaces over n#CP^2 with algebraic dimension 2 have either empty or single fundamental system.
Research nearly Kähler structures on 6-sphere using twistor bundle sections.
problem Finding nearly Kähler structures on the 6-sphere.
method Analyzing sections of a twistor bundle to identify nearly Kähler structures.
result Existence of 1-parametric families of sections giving nearly Kähler structures on the sphere.
Effective action for Kerr-Newman black hole found in twistor theory.
problem Effective action for Kerr-Newman black hole.
method Twistor particle theory to achieve all-orders worldline effective action.
result Exact hidden symmetries identified in self-dual backgrounds.
Researchers develop new symmetry operators from conformal Killing-Yano forms.
problem Constructing symmetry operators for twistor spinors in conformally-flat backgrounds.
method Using conformal Killing-Yano forms and graded Lie algebra structure, the researchers extended conformal superalgebras to include twistor spinors.
result Extended conformal superalgebras that include twistor spinors and conformal Killing-Yano forms are constructed.
In this paper we discuss the twistor equation in Lorentzian spin geometry. In particular, we explain the local conformal structure of Lorentzian manifolds, which admit twistor spinors inducing lightlike Dirac currents. Furthermore, we derive all local geometries with singularity free twistor spinors that occur up to di…
Skew algebroids on twistor spaces help understand bihermitian manifolds.
problem Understanding bihermitian manifolds.
method Introducing skew algebroids on twistor spaces.
result Derives results about bihermitian manifolds.
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 discuss two natural almost complex structures on such a twistor space and their ho…
This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space-time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the 6-dimensional case in which twisto…
The paper establishes a connection between superminimal surfaces and Lagrangian submanifolds in twistor spaces.
problem Understanding the geometric relationship between superminimal surfaces and Lagrangian submanifolds in twistor spaces.
method Proves a bijective correspondence between superminimal surfaces and Lagrangian submanifolds of twistor spaces, using specific constructions and projections.
result Produces many Lagrangian submanifolds of twistor spaces that are also minimal.
Generalizes twistor lines for complex tori, introducing new non-compact curves.
problem Understanding the structure of complex tori through twistor lines.
method Introducing and studying two new types of non-compact analytic curves in the period domain of complex tori.
result Analytic properties of compactifications of curves, preservation of cohomology classes, and twistor path connectivity.
The abstract extends twistor construction to manifolds with generalized metrics.
problem Extending twistor construction to manifolds with generalized metrics.
method Defining generalized twistor space and finding integrability conditions for intrinsic isomorphisms.
result Existence of intrinsic isomorphisms in generalized twistor spaces.
It is shown that there exist non-singular cubic surfaces in CP^3 containing 5 twistor lines. This is the maximum number of twistor fibres that a non-singular cubic can contain. Cubic surfaces in CP^3 with 5 twistor lines are classified up to transformations preserving the conformal structure of S^4.
Biholomorphisms of transport twistor spaces are rigid under certain conditions.
problem Rigidity of biholomorphisms in transport twistor spaces.
method Proof of rigidity for biholomorphisms between transport twistor spaces of simple or Anosov surfaces.
result Biholomorphisms are rigid, up to constant rescaling and the antipodal map, being lifts of orientation-preserving isometries.
Study geometric structures on twistor and reflector spaces of paraquaternionic contact manifolds.
problem Geometric structures on paraquaternionic contact manifolds.
method Investigate fiber bundles (twistor and reflector spaces) over paraquaternionic contact manifolds.
result Intrinsic geometric structures on twistor and reflector spaces are always integrable.
Twistor lines connect complex tori in their period domain.
problem Connecting complex tori in their period domain.
method Analyzing twistor lines in the period domain of complex tori.
result Periods of complex tori can be joined by generic chains of twistor lines.
We deal here with the geometry of the twistor fibration $\mathcal{Z} \to \bb{S}^3_1$ over the De Sitter 3-space. The total space Z is a five dimensional reductive homogeneous space with two canonical invariant almost CR structures. Fixed the normal metric on Z we study the harmonic map equation …
Study of complex structures on product twistor spaces for 4D manifolds.
problem Understanding complex structures on product twistor spaces.
method Analyzing the product bundle of twistor spaces with Riemannian metrics and almost complex structures.
result Determined Gray-Hervella classes for 4D manifolds.
The paper studies four Hermitian structures on twistor spaces.
problem Understanding the geometry of Hermitian surfaces via twistor spaces.
method Defining four almost Hermitian structures on twistor spaces using canonical connections.
result Relations between twistor space geometry and Hermitian surface geometry.
We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex structures. Moreover, in the strong HKT case we construct a metric and three comp…
Study Moishezon twistor spaces using quartic hypersurfaces and Del Pezzo fibrations.
problem Classify Moishezon twistor spaces with specific half-anti-canonical systems.
method Utilize pluri-half-anti-canonical maps and quartic hypersurfaces to investigate twistor spaces.
result Complete classification of Moishezon twistor spaces with half-anti-canonical systems as pencils.
The paper connects complex spacetimes to twistor spaces and finds an almost contact structure.
problem Understanding the geometry of complex spacetimes and their relation to twistor spaces.
method Using a correspondence between 5D complex spacetimes and 4D twistor spaces, the paper constructs almost contact structures.
result A 5-dimensional K-contact manifold can be derived from the Ren-Wang twistor space.
Extended superalgebras from twistor and Killing spinors in constant curvature and Einstein manifolds.
problem Constructing extended superalgebras from twistor and Killing spinors.
method Using twistor and Killing spinors, symmetry operators, and KY/CKY forms, extended superalgebras are constructed.
result Extended Killing and conformal superalgebras are constructed in constant curvature and Einstein manifolds.
Study on surfaces containing twistor lines, proving their density and bounds.
problem Understanding the distribution and maximum number of twistor lines on algebraic surfaces.
method Analyzing ideal sheaves, proving density in Grassmannian, and calculating bounds for surface degrees.
result Twistor lines are Zariski dense in the Grassmannian and have maximum bounds on their number.
The quaternion twistor space of a hyperkähler manifold can carry both Kähler and non-Kähler structures.
problem Finding compact manifolds that can carry both Kähler and non-Kähler complex structures.
method Reviewing twistor techniques and constructing examples of manifolds with mixed structures.
result The quaternion twistor space of a hyperkähler manifold admits both Kähler and non-Kähler structures.
We develop a non-relativistic twistor theory, in which Newton--Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O⊕O(2). We show that the Newton--Cartan space-times are unstable under the general K…
New method solves 'googly problem' for Schwarzschild black holes.
problem Solving the 'googly problem' for non-chiral field configurations.
method Using twistor space and holomorphic loci to construct a non-self-dual, four-dimensional Kähler metric.
result First instance of a non-self-dual Einstein metric from holomorphic data in twistor space.
The LeBrun-Mason twistor correspondences for S1-invariant self-dual Zollfrei metrics are explicitly established. We give explicit formulas for the general solutions of the wave equation and the monopole equation on the de Sitter three-space under the assumption for the tameness at infinity by using Radon-type integr…
We give a self-contained derivation of the MHV amplitudes for gravity and use the associated twistor generating function to define a twistor action for the MHV diagram approach to gravity. Starting from a background field calculation on a spacetime with anti self-dual curvature, we obtain a simple spacetime formula for…
Achieved all-orders worldline action for Kerr black hole.
problem Calculating effective action for Kerr black hole.
method Twistor particle theory.
result All-orders worldline effective action for Kerr black hole.
New method recovers hyperkähler metrics from twistor models.
problem Constructing and recovering hyperkähler metrics from twistor models.
method Construction of principal twistor models and universality theorem.
result Universality theorem for recovering hyperkähler metrics from twistor spaces.