Further Advances in Twistor Theory Volumn III Curved Twistor Spaces 1st Edition by L J Mason ISBN 113843034X 9781138430341

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ISBN 10: 113843034X 

ISBN 13: 9781138430341

Author: L.J. Mason

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:

PART 1: THE NONLINEAR-GRAVITON AND RELATED CONSTRUCTIONS

• Chapter 1: The Nonlinear Graviton and Related Construction, L.H. Mason

• Chapter 2: The Good Cut Equation Revisited, K.P. Tod

• Chapter 3: Sparling-Tod Metric = 3D Eguchi Hanson, G. Burnett-Stuart

• Chapter 4: The Wave Equation Transfigured, C.R. LeBrun

• Chapter 5: Conformal Killing Vectors and Reduced Twistor Spaces, P.E. Jones

• Chapter 6: An Alternative Interpretation of some Nonlinear Graviton, P.E. Jones

• Chapter 7: H-Space from a Different Direction, C.N. Kazameh and E.T. Newman

• Chapter 8: Complex Quaternionic Kähler Manifolds, M.G. Eastwood

• Chapter 9: A.L.E. Gravitational Instantons and the Icosahedron, P.B. Kronheimer

• Chapter 10: The Einstein Bundle of a Nonlinear Graviton, M.G. Eastwood

• Chapter 11: Example of Anti-Self-Dual Metrics, C.R. LeBrun

• Chapter 12: Some Quaternionically Equivalent Einstein Metrics, A.F. Swann

• Chapter 13: On the Topology of Quaternionic Manifolds, C.R. LeBrun

• Chapter 14: Homogeneity of Twistor Spaces, A.F. Swann

• Chapter 15: The Topology of Anti-Self-Dual 4-Manifolds, C.R. LeBrun

• Chapter 16: Metrics with SD Weyl Tensor from Painlevé-VI, K.P. Tod

• Chapter 17: Indefinite Conformally-ASD Metrics on S² x S², K.P. Tod

• Chapter 18: Cohomology of a Quaternionic Complex, R. Horan

• Chapter 19: Conformally Invariant Differential Operators on Spin Bundles, M.G. Eastwood

• Chapter 20: A Twistorial Construction of (1,1)-Geodesic Maps, P.Z. Kobak

• Chapter 21: Exceptional HyperKähler Reductions, P.Z. Kobak and A.F. Swann

• Chapter 22: A Nonlinear Graviton from the Sine-Gordon Equation, M. Dunajski

• Chapter 23: A Recursion Operator for ASD Vacuums and ZRM Fields on ASD Background, M. Dunajski and L.J. Mason

PART 2: SPACES OF COMPLEX NULL GEODESICS

• Chapter 1: Introduction to Spaces of Complex Null Geodesics, L. Mason

• Chapter 2: Null Geodesics and Conformal Structures, C.R. LeBrun

• Chapter 3: Complex Null Geodesics in Dimension Three, C.R. LeBrun

• Chapter 4: Null Geodesics and Contact Structure, C.R. LeBrun

• Chapter 5: Heaven with a Cosmological Constant, C.R. LeBrun

• Chapter 6: Some Remakes on Non-Abelian Sheaf Cohomology, M.G. Eastwood

• Chapter 7: Formal Thickenings of Ambitwistors for Curved Space-Times, C.R. LeBrun

• Chapter 8: Superambitwistors, N.G. Eastwood

• Chapter 9: Formal Neighbourhoods, Supermanifolds and Relativised Algebras, R. Baston

• Chapter 10: Quaternionic Geometry and the Future Tube, C.R. LeBrun

• Chapter 11: Deformation of Ambitwistor Space and Vanishing Bach Tensors, R.H. Baston and L.J. Mason

• Chapter 12: Formal Neighbourhoods for Curved Ambitwistors, R.J. Baston and L.J. Mason

• Chapter 13: Towards an Ambitwistor Description of Gravity, J. Isenberg and P. Yasskin

PART 3: HYPERSURFACE TWISTORS AND CAUCHY-RIEMANN STRUCTURES

• Chapter 1: Introduction to Hypersurface Twistors and Cauchy-Riemann Structure, L.J. Mason

• Chapter 2: A Review of Hypersurface Twistors, R.S. Ward

• Chapter 3: Twistor CR Manifolds, C.R. LeBrun

• Chapter 4: Twistor CR Structure and Initial Data, C.R. LeBrun

• Chapter 5: Visualizing Twistor CR Structures, C.R. LeBrun

• Chapter 6: The Twistor Theory of Hypersurfaces in Space-Time, G.A.J. Sparling

• Chapter 7: Twistors, Spinors, and the Einstein Vacuum Equations, G.A.J. Sparling

• Chapter 8: Einstein Vacuum Equations, G.A.J. Sparling

• Chapter 9: On Bryant’s Condition for Holomorphic Curves in CR-Spaces, R. Penrose

• Chapter 10: The Hill-Penrose-Sparling C.R.-Folds, M.G. Eastwood

• Chapter 11: The Structure and Evolution of Hypersurfaces Twistor Spaces, L.J. Mason

• Chapter 12: The Chern-Moser Connection for Hypersurface Twistor CR Manifolds, L.J. Mason

• Chapter 13: The Constraint and Evolution Equations for Hypersurface CR Manifolds, L.J. Mason

• Chapter 14: A Characterization of Twistor CR Manifold, L.J. Mason

• Chapter 15: The Kähler Structure on Asymptotic Twistor Space, L.H. Mason

• Chapter 16: Twistor Cauchy-Riemann Manifolds for Algebraically Special Space-Times, L.H. Mason

• Chapter 17: Causal Relations and Linking in Twistor Space, R. Low

• Chapter 18: Hypersurface Twistors, L.H. Mason

• Chapter 19: A Twistorial Approach to the Full Vacuum Equations, L.H. Mason and R. Penrose

• Chapter 20: A Note on Causal Relations and Twistor Space, R. Low

PART 4: TOWARDS A TWISTOR DESCRIPTION OF GENERAL SPACE-TIMES

• Chapter 1: Towards a Twistor Description of General Space-Times; Introductory Comments, R. Penrose

• Chapter 2: Remarks on the Sparling and Eguchi-Hanson (Googly?) Gravitons

• Chapter 3: A New Angle on the Googly Graviton, R. Penrose

• Chapter 4: Concerning a Fourier Contour Integral, R. Penrose

• Chapter 5: The Googly Maps for the Eguchi-Hanson/Sparling-Tod Graviton, P.R. Law

• Chapter 6: Physical Left-Right Symmetry and Googlies, R. Penrose

• Chapter 7: On the Geometry of Googly Maps, R. Penrose and P.R. Law

• Chapter 8: A Prosaic Approach to Googlies, A. Helfer

• Chapter 9: More on Googlies, A. Helfer

• Chapter 10: A Note on Sparling’s 3-Form, R. Penrose

• Chapter 11: Remarks on Curved-Space Twistor Theory and Googlies, R. Penrose

• Chapter 12: Relative Cohomology, Googlies, and Deformations of I, R. Penrose

• Chapter 13: Is the Plebanski Viewpoint Relevant to the Googly Problem? G. Burnett-Stuart

• Chapter 14: Note on the Geometry of the Googly Mappings, P. Law

• Chapter 15: Exponentiating a Relative H², R. Penrose

• Chapter 16: The Complex Structure of Deformed Twistor Space, P. Law

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Tags: L J Mason, Further Advances, Twistor Theory, Curved Twistor Spaces