Further Advances in Twistor Theory: v. 3

Further Advances in Twistor Theory: v. 3 : Curved Twistor Spaces

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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.show more

Product details

  • Paperback | 432 pages
  • 155.7 x 233.7 x 23.4mm | 656.9g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • United States
  • English
  • 50 black & white illustrations
  • 1584880473
  • 9781584880479

Review quote

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

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 Kahler 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 Painleve-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 HyperKahler 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 Kahler 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. Lawshow more

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