A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study of complex tori using twistor triangles and algebraic representations.
The study generalizes twistor spinors to Kähler manifolds and finds bilinear form equations.
We consider gauged twistor spinors which are supersymmetry generators of supersymmetric and superconformal field theories in curved backgrounds. We show that the spinor bilinears of gauged twistor spinors satify the gauged conformal Killing-Yano equation. We prove that the symmetry operators of the gauged twistor spino…
2D twistor manifolds explain Teukolsky equations for rotating black holes.
The paper proves unique properties of Riemannian twistor spaces under specific curvature conditions.
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…
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.
We review aspects of twistor theory, its aims and achievements spanning thelast five decades. In the twistor approach, space--time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three--fold -- the twistor space. After giving an elementary construction of this s…
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.
The paper examines curvature properties of twistor spaces.
Study on surfaces in flag threefold with constraints on twistor fibers.
Develops twistor theory for foliated manifolds, proving orbifold results.
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.
Napoleonic triangles don't exist in hyperbolic geometry.
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…
Effective action for Kerr-Newman black hole found in twistor theory.
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…
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.
Generalizes twistor lines for complex tori, introducing new non-compact curves.
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.
New bounds on inscribed triangles in arbitrary planar domains.
We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting symmetry operators of twistor spinors. Conformal superalgebras which consist of …
Biholomorphisms of transport twistor spaces are rigid under certain conditions.
Study geometric structures on twistor and reflector spaces of paraquaternionic contact manifolds.
Study on Laplacian determinant in isosceles triangles, finding equilateral triangle minimizes determinant.
Symmetry operators of twistor spinors and harmonic spinors can be constructed from conformal Killing-Yano forms. Transformation operators relating twistors to harmonic spinors are found in terms of potential forms. These constructions are generalized to gauged twistor spinors and gauged harmonic spinors. The operators …
Paper calculates eigenvalues of a specific triangle on a sphere.
Twistor lines connect complex tori in their period domain.
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 is a five dimensional reductive homogeneous space with two canonical invariant almost CR structures. Fixed the normal metric on we study the harmonic map equation …
Study of complex structures on product twistor spaces for 4D manifolds.
New method shows any triangle group generating pair is related to special coverings.
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…
Shorter sides in geodesic triangles in hyperbolic plane.
Study Moishezon twistor spaces using quartic hypersurfaces and Del Pezzo fibrations.
The paper connects complex spacetimes to twistor spaces and finds an almost contact structure.
The study proves conditions for triangle comparison on surfaces of revolution.
Complex hyperbolic triangle groups were first considered by Mostow in building the first nonarithmetic lattices in PU(2, 1). They are a natural generalization of the classical triangle groups acting on the hyperbolic plane. A well-known theorem of Takeuchi is that there are only finitely many Fuchsian triangle groups t…
The paper explores isotopic triples of triangles in 3D space.
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 . We show that the Newton--Cartan space-times are unstable under the general K…
New method solves 'googly problem' for Schwarzschild black holes.
The LeBrun-Mason twistor correspondences for -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…
Achieved all-orders worldline action for Kerr black hole.
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…