Further Advances in Twistor Theory, Volume III : Curved Twistor Spaces book cover
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Further Advances in Twistor Theory, Volume III
Curved Twistor Spaces




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ISBN 9781584880479
Published March 15, 2001 by Chapman and Hall/CRC
432 Pages - 50 B/W Illustrations

 
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Book Description

Although twistor theory originated as an approach to the unification of quantum theory and general relativity, twistor correspondences and their generalizations have provided powerful mathematical tools for studying problems in differential geometry, nonlinear equations, and representation theory. At the same time, the theory continues to offer promising new insights into the nature of quantum theory and gravitation.

Further Advances in Twistor Theory, Volume III: Curved Twistor Spaces is actually the fourth in a series of books compiling articles from Twistor Newsletter-a somewhat informal journal published periodically by the Oxford research group of Roger Penrose. Motivated both by questions in differential geometry and by the quest to find a twistor correspondence for general Ricci-flat space times, this volume explores deformed twistor spaces and their applications.

Articles from the world's leading researchers in this field-including Roger Penrose-have been written in an informal, easy-to-read style and arranged in four chapters, each supplemented by a detailed introduction. Collectively, they trace the development of the twistor programme over the last 20 years and provide an overview of its recent advances and current status.

Table of Contents

THE NONLINEAR-GRAVITON AND RELATED CONSTRUCTIONS
The Nonlinear Graviton and Related Construction, L.H. Mason
The Good Cut Equation Revisited, K.P. Tod
Sparling-Tod Metric = 3D Eguchi Hanson, G. Burnett-Stuart
The Wave Equation Transfigured, C.R. LeBrun
Conformal Killing Vectors and Reduced Twistor Spaces, P.E. Jones
An Alternative Interpretation of some Nonlinear Graviton, P.E. Jones
H-Space from a Different Direction, C.N. Kazameh and E.T. Newman
Complex Quaternionic Kähler Maniforlds, M.G. Eastwood
A.L.E. Gravitational Instatons and the Icosahedron, P.B. Kronheimer
The Einstein Bundle of a Nonlinear Graviton, M.G. Eastwood
Example of Anti-Self-Dual Metrics, C.R. LeBrun
Some Quaternionically Equivalent Einstein Metrics, A.F. Swann
On he Topology of Quaternionic Manifolds, C.R. LeBrun
Homogeneity of Twistor Spaces, A.F. Swann
The Topology of Anti-Self-Dual 4-Manifolds, C.R. LeBrun
Metrics with SD Weyl Tensor from Painlevé-VI, K.P. Tod
Indefinite Conformally-ASD Metrics on S2 x S2, K.P. Tod
Cohomology of a Quaternionic Complex, R. Horan
Conformally Invariant Differential Operators on Spin Bundles, M.G. Eastwood
A Twistorial Construction of (1,1)-Geodesic Maps, P.Z. Kobak
Exceptional HyperKähler Reductions, P.Z. Kobak and A.F. Swann
A Nonlinear Graviton from the Sine-Gordon Equation, M. Dunajski
A Recursion Operator for ASD Vacuums and ZRM Fields on ASD Background, M. Dunaski and L.J. Mason
SPACES OF COMPLEX NULL GEODESICS
Introduction to Spaces of Complex Null Geodesic, L. Mason
Null Geodesics and Conformal Structures, C.R. LeBrun
Complex Null Geodesics in Dimension Three, C.R. LeBrun
Null Geodesics and Contact Structure, C.R. LeBrun
Heaven with a Cosmological Constant, C.R. LeBrun
Some Remakes on Non-Abelian Sheaf Cohomology, M.G. Eastwood
Formal Thickenings of Ambitwistors for Curved Space-Times, C.R. LeBrun
Superambitwistors, N.G. Eastwood
Formal Neighbourhoods, Supermanifolds and Relativised Algebras, R. Baston
Quaternionic Geometry and the Future Tube, C.R. LeBrun
Deformation of Ambitwistor Space and Vanishing Bach Tensors, R.H. Baston and L.J. Mason
Formal Neighbourhoods for Curved Ambitwistors, R.J. Baston and L.J. Mason
Towards and Ambitwistor Description of Gravity, J. Isenberg and P. Yasskin
HYPERSURFACE TWISTORS AND CAUCHY-RIEMANN STRUCTURES
Introduction to Hypersurface Twistors and Cauchy-Riemann Structure, L.J. Mason
A Review of Hypersuface Twistors, R.S. Ward
Twistor CR Manifolds, C.R. LeBrun
Twistor CR Structure and Initial Data, C.R. LeBrun
Visualizing Twistor CR Structures, C.R. LeBrun
The Twistor Theory of Hypersurfaces in Space-Time, G.A.J. Sparling
Twistors, Spinors, and the Einstein Vacuum Equations, G.A.J. Sparling
Einstein Vacuum Equations, G.A.J. Sparling
On Bryant's Condition for Holomorphic curves in CR-Spaces, R. Penrose
The Hill-Penrose-Sparling C.R.-Folds, M.G. Eastwood
The Structure and Evolution of Hypersurfaces Twistor Spaces, L.J. Mason
The Chern-Moser Connection for Hypersurface Twistor CR Manifolds, L.J. Mason
The constraint and Evolution Equations for Hypersurface CR Manifolds, L.J. Mason
A Characterization of Twistor CR Manifold, L.J. Mason
The Kähler Structure on Asymptotic Twistor Space, L.H. Mason
Twistor Cauchy-Riemann Manifolds for Algebraically Special Space-Times, L/H. Mason
Causal Relations and Linking in Twistor Space, R. Low
Hypersurface Twistors, L.H. Mason
A Twistorial Approach to the full Vacuum Equations, L.H. Mason and R. Penrose
A Note on Causal Relations and Twistor Space, R. Low
TOWARDS A TWISTOR DESCRIPTION OF GENERAL SPACE TIMES
Towards a Twistor Description of General Space-Times; Introductory Comments, R. Penrose
Remarks on the Sparling and Eguchi-Hanson (Googly?) Gravitons
A New Angle on the Googly Graviton, R. Penrose
Concerning a Fourier Contour Integral, R. Penrose
The Googly Maps for the Eguchi-Hanson/Sparling-Tod Graviton, P.R. Law
Physical Left-Right Symmetry and Googlies, R. Penrose
On the Geometry of Googly Maps, R. Penrose and P.R. Law
A Prosaic Approach to Googlies, A. Helfer
More on Googlies, A. Helfer
A Note on Sparling's 3-Form, r. Penrose
Remarks on Curved-Space Twistor Theory and Googlies, R. Penrose
Relative Cohomology, Googlies, and Deformations of I, R. Penrose
Is the Plebanski Viewpoint Relevant to the Googly Problem? G. Burnett-Stuart
Note on the Geometry of the Googly Mappings, P. Law
Exponentiating a Relative H2, R. Penrose
The Complex Structure of Deformed Twstor Space, P. Law

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Editor(s)

Biography

St Peter’s College and the Mathematical Institute, Oxford, King’s College London, Instytut Matematyki, Uniwersytet Jagielloński Kraków, Center for Mathematical Sciences, Munich University of Technology, Munich

Reviews

"… In summary, these articles contain many interesting facts and provocative ideas that do not otherwise appear in the published literature."
-Mathematical Reviews