Extensionalism and Twistor Space: Similarities and Relations between Art and Twistor Theory

Leonardo ◽  
1995 ◽  
Vol 28 (3) ◽  
pp. 177 ◽  
Author(s):  
Fre Ilgen
Keyword(s):  
Twistor Space ◽  
Twistor Theory

Duality in twistor theory without Minkowski space

1985 ◽  
Vol 98 (3) ◽  
pp. 591-600
Author(s):  
M. A. Singer
Keyword(s):  
Minkowski Space ◽  
Twistor Space ◽  
Alternative Proof ◽  
Twistor Theory ◽  
Set Up

AbstractA modified form of the generalized Penrose-Ward Transform [4, 6] is set up to investigate the correspondence between twistor space and dual twistor space. The ways in which it differs from the ‘usual’ transform are discussed and it is used to give an alternative proof of Eastwood's recent generalization [7] of the twistor transform [9, 5] which avoids all mention of Minkowski space.

Twistor theory and the energy—momentum and angular momentum of the gravitational field at spatial infinity

1983 ◽  
Vol 390 (1798) ◽  
pp. 191-215 ◽  
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Twistor Space ◽  
Conserved Quantities ◽  
Twistor Theory ◽  
Coordinate Transformations ◽  
Spatial Infinity ◽  
Weyl Curvature ◽  
Linearized Theory ◽  
Math Phys

Penrose’s ‘quasi-local mass and angular momentum’ (Penrose, Proc. R. Soc. Lond . A 381, 53 (1982)) is investigated for 2-surfaces near spatial infinity in both linearized theory on Minkowski space and full general relativity. It is shown that for space-times that are radially smooth of order one in the sense of Beig & Schmidt ( Communs math. Phys . 87, 65 (1982)), with asymptotically electric Weyl curvature, there exists a global concept of a twistor space at spatial infinity. Global conservation laws for the energy—momentum and angular momentum are obtained, and the ten conserved quantities are shown to be invariant under asymptotic coordinate transformations. The relation to other definitions is discussed briefly.

scholarly journals Twistor spaces on foliated manifolds

2021 ◽  
pp. 2150056
Author(s):  
Rouzbeh Mohseni ◽  
Robert A. Wolak
Keyword(s):  
Normal Bundle ◽  
Twistor Space ◽  
Riemannian Foliation ◽  
Holomorphic Mappings ◽  
Twistor Theory ◽  
Simple Consequence ◽  
Twistor Spaces ◽  
Leaf Space ◽  
Foliated Manifolds ◽  
Theory Lead

The theory of twistors on foliated manifolds is developed. We construct the twistor space of the normal bundle of a foliation. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate and prove foliated versions of some well-known results on holomorphic mappings. Since any orbifold can be understood as the leaf space of a suitably defined Riemannian foliation we obtain orbifold versions of the classical results as a simple consequence of the results on foliated mappings.

An Introduction to Twistor Theory

1994 ◽  
Author(s):  
S. A. Huggett ◽  
K. P. Tod
Keyword(s):  
Twistor Theory

scholarly journals Generalized almost even-Clifford manifolds and their twistor spaces

2021 ◽  
Vol 8 (1) ◽  
pp. 96-124
Author(s):  
Luis Fernando Hernández-Moguel ◽  
Rafael Herrera
Keyword(s):  
Twistor Space ◽  
Complex Structure ◽  
Twistor Spaces ◽  
Recent Interest ◽  
Generalized Complex Structure ◽  
Generalized Complex ◽  
Space Construction ◽  
Clifford Structures

Abstract Motivated by the recent interest in even-Clifford structures and in generalized complex and quaternionic geometries, we introduce the notion of generalized almost even-Clifford structure. We generalize the Arizmendi-Hadfield twistor space construction on even-Clifford manifolds to this setting and show that such a twistor space admits a generalized complex structure under certain conditions.

scholarly journals The Adjunction Inequality for Weyl-Harmonic Maps

2020 ◽  
Vol 7 (1) ◽  
pp. 129-140
Author(s):  
Robert Ream
Keyword(s):  
Minimal Surfaces ◽  
Twistor Space ◽  
Harmonic Maps ◽  
Holomorphic Curves ◽  
Weyl Connection ◽  
Almost Kähler ◽  
Conformal Manifolds

AbstractIn this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical 𝒥-holomorphic curves in the weightless twistor space and branched Weyl-minimal surfaces. When (M, c, J) is conformally almost-Hermitian, there is a canonical Weyl connection. We show that for the canonical Weyl connection, branched Weyl-minimal surfaces satisfy the adjunction inequality\chi \left( {{T_f}\sum } \right) + \chi \left( {{N_f}\sum } \right) \le \pm {c_1}\left( {f*{T^{\left( {1,0} \right)}}M} \right).The ±J-holomorphic curves are automatically Weyl-minimal and satisfy the corresponding equality. These results generalize results of Eells-Salamon and Webster for minimal surfaces in Kähler 4-manifolds as well as their extension to almost-Kähler 4-manifolds by Chen-Tian, Ville, and Ma.

scholarly journals Philosophical Aspects of Astrobiology Revisited

Philosophies ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 55
Author(s):  
Rainer E. Zimmermann
Keyword(s):  
Dynamical Systems ◽  
First Principles ◽  
Special Form ◽  
Mathematical Representation ◽  
Dynamical Structure ◽  
Twistor Theory ◽  
Fundamental Physics ◽  
Physical Universe ◽  
The World ◽  
Traditional Sense

Given the idea that Life as we know it is nothing but a special form of a generically underlying dynamical structure within the physical Universe, we try to introduce a concept of Life that is not only derived from first principles of fundamental physics, but also metaphysically based on philosophical assumptions about the foundations of the world. After clarifying the terminology somewhat, especially with a view to differentiating reality from modality, we give an example for a mathematical representation of what the substance of reality (in the traditional sense of metaphysics) could actually mean today, discussing twistor theory as an example. We then concentrate on the points of structural emergence by discussing the emergence of dynamical systems and of Life as we know it, respectively. Some further consequences as they relate to meaning are discussed in the end.

scholarly journals The Weyl double copy from twistor space

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Erick Chacón ◽  
Silvia Nagy ◽  
Chris D. White
Keyword(s):  
Exact Solutions ◽  
Twistor Space ◽  
Current Form ◽  
New Formalism ◽  
Petrov Types ◽  
Gravity Theories ◽  
Double Copy

Abstract The Weyl double copy is a procedure for relating exact solutions in biadjoint scalar, gauge and gravity theories, and relates fields in spacetime directly. Where this procedure comes from, and how general it is, have until recently remained mysterious. In this paper, we show how the current form and scope of the Weyl double copy can be derived from a certain procedure in twistor space. The new formalism shows that the Weyl double copy is more general than previously thought, applying in particular to gravity solutions with arbitrary Petrov types. We comment on how to obtain anti-self-dual as well as self-dual fields, and clarify some conceptual issues in the twistor approach.

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