Twistor Theory of Dancing Paths
نویسندگان
چکیده
Given a path geometry on surface $\mathcal{U}$, we construct causal structure four-manifold which is the configuration space of non-incident pairs (point, path) $\mathcal{U}$. This corresponds to conformal if and only $\mathcal{U}$ real projective plane, paths are lines. We give example given by symmetric sextic, an ${\rm SL}(2,{\mathbb R})$-invariant where ellipses area $\pi$ centred at origin. shall also discuss seven-dimensional manifold corresponding conic) plane.
منابع مشابه
Twistor Theory
Twistor theory began with the work of Roger Penrose who introduced the powerful techniques of complex algebraic geometry into general relativity. Loosely speaking it is the use of complex analytic methods to solve problems in real differential geometry. In most cases the emphasis is on the geometry of the problem rather than the analysis. My lectures are not designed to be a survey of all of tw...
متن کاملTwistor Theory of Symplectic Manifolds
November 2004 Abstract This article is a contribuition to the understanding of the geometry of the twistor space of a symplectic manifold. We consider the bundle Z l with fibre the Siegel domain Sp(2n,R)/U(n) existing over any given symplectic manifold M . Then, while recalling the construction of the celebrated almost complex structure induced on Z l by a symplectic connection on M , we study ...
متن کاملHeterotic Twistor-String Theory
We reformulate twistor-string theory as a heterotic string based on a twisted (0,2) model. The path integral localizes on holomorphic maps, while the (0,2) moduli naturally correspond to the states of N = 4 super Yang-Mills and conformal supergravity under the Penrose transform. We show how the standard twistor-string formulae of scattering amplitudes as integrals over the space of curves in su...
متن کاملTwistor Theory of Pseudoholomorphic Curves
A twistor theory of pseudoholomorphic curves in 4–manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with, and yields many analogues of results in complex surface theory, using a description of the local geometry via Cartan’s method of equivalence. Twistor theory then un...
متن کاملTwistor theory at fifty: from contour integrals to twistor strings.
We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space-time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold-the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Symmetry Integrability and Geometry-methods and Applications
سال: 2022
ISSN: ['1815-0659']
DOI: https://doi.org/10.3842/sigma.2022.027