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E-raamat: Further Advances in Twistor Theory, Volume III: Curved Twistor Spaces

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Twistor theory originated as an approach to unifying quantum theory and general relativity by reformulating basic physics in terms of the geometry of twistor space. Its aspirations remain unfilled, but it has provided some mathematical tools for studying problems in differential geometry, nonlinear equations, and other areas. The volume here is actually the fourth collection of articles reprinted from Twistor Newsletter , a photocopied and partly handwritten journal published occasionally since 1976 by members of Roger Penrose's research group in Oxford. The 89 papers cover the nonlinear graviton and related constructions, spaces of complex null geodesics, hypersurface twistors and Cauchy-Riemann manifolds, and towards a twistor description of general space-time. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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.

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

The nonlinear graviton and related constructions The Nonlinear Graviton and Related Constructions 1(8) L.J. Mason The Good Cut Equation Revisited 9(5) K.P. Tod Sparling-Tod Metric = Eguchi-Hanson 14(3) G. Burnett-Stuart The Wave Equation Transfigured 17(3) C.R. LeBrun Conformal Killing Vectors and Reduced Twistor Spaces 20(5) P.E. Jones An Alternative Interpretation of Some Nonlinear Gravitons 25(4) P.E. Jones H-Space from a Different Direction 29(2) C.N. Kozameh E.T. Newman Complex Quaternionic Kahler Manifolds 31(3) M.G. Eastwood A.L.E. Gravitational Instantons and the Icosahedron 34(2) P.B. Kronheimer The Einstein Bundle of a Nonlinear Graviton 36(3) M.G. Eastwood Examples of Anti-Self-Dual Metrics 39(6) C.R. LeBrun Some Quaternionically Equivalent Einstein Metrics 45(3) A.F. Swann On the Topology of Quaternionic Manifolds 48(2) C.R. LeBrun Homogeneity of Twistor Spaces 50(3) A.F. Swann The Topology of Anti-Self-Dual 4-Manifolds 53(6) C.R. LeBrun Metrics with S.D. Weyl Tensor from Painleve- VI 59(4) K.P. Tod Indefinite Conformally-A. S. D. Metrics on S2 X S2 63(3) K.P. Tod Cohomology of a Quaternionic Complex 66(6) R. Horan Conformally Invariant Differential Operators on Spin Bundles 72(3) M.G. Eastwood A Twistorial Construction of (1,1)-Geodesic Maps 75(6) P.Z. Kobak Exceptional Hyper-Kahler Reductions 81(4) P.Z. Kobak A.F. Swann A Nonlinear Graviton from the Sine-Gordon Equation 85(3) M. Dunajski A Recursion Operator for A.S.D. Vacuums and ZRM Fields on A.S.D. Backgrounds 88(9) M. Dunajski L.J. Mason Spaces of Complex null geodesics Introduction to Spaces of Complex Null Geodesics 97(5) L.J. Mason Null Geodesics and Conformal Structures 102(6) C.R. LeBrun Complex Null Geodesics in Dimension Three 108(3) C.R. LeBrun Null Geodesics and Conformal Structures 111(1) C.R. LeBrun Heaven with a Cosmological Constant 112(1) C.R. LeBrun Some Remarks on Non-Abelian Sheaf Cohomology 113(2) M.G. Eastwood Superstructure versus Formal Neighbourhoods 115(2) M.G. Eastwood Formal Thickenings of Ambitwistors for Curved Space-Time 117(6) M.G. Eastwood Deformations of Ambitwistor Space 123(4) L.J. Mason Ambitwistors and Yang-Mills Fields in Self-Dual Space-Times 127(3) C.R. LeBrun Superambitwistors 130(2) M.G. Eastwood Formal Neighbourhoods, Supermanifolds and Relativised Algebras 132(6) R.J. Baston Quaternionic Geometry and the Future Tube 138(2) C.R. LeBrun Deformation of Ambitwistor Space and Vanishing Bach Tensors 140(2) R.J. Baston L.J. Mason Formal Neighbourhoods for Curved Ambitwistors 142(8) R.J. Baston L.J. Mason Towards an Ambitwistor Description of Gravity 150(9) J. Isenberg P. Yasskin Hypersurface twistors and Cauchy-Riemann manifolds Introduction to Hypersurface Twistors and Cauchy-Riemann Structures 159(4) L. Mason A Review of Hypersurface Twistors 163(3) R.S. Ward Twistor CR Manifolds 166(4) C.R. LeBrun Twistor CR Structures and Initial Data 170(3) C.R. LeBrun Visualizing Twistor CR Structures 173(2) C.R. LeBrun The Twistor Theory of Hypersurfaces in Space-Time 175(4) G.A.J. Sparling Twistor, Spinors and the Einstein Vacuum Equations 179(8) G.A.J. Sparling Einstein Vacuum Equations 187(5) G.A.J. Sparling On Bryants Condition for Holomorphic Curves in CR-Spaces 192(2) R. Penrose The Hill-Penrose-Sparling C.R.-Folds 194(1) M.G. Eastwood The Structure and Evolution of Hypersurface Twistor Spaces 195(7) L.J. Mason The Chern-Moser Connection for Hypersurface Twistor CR Manifolds 202(7) L.J. Mason The Constraint and Evolution Equations for Hypersurface CR Manifolds 209(2) L.J. Mason A Characterization of Twistor CR Manifolds 211(4) L.J. Mason The Kahler Structure on Asymptotic Twistor Space 215(1) L. Mason Twistor CR manifolds for Algebraically Special Space-Times 216(6) L.J. Mason Causal Relations and Linking in Twistor Space 222(2) R. Low Hypersurface Twistors 224(6) L.J. Mason A Twistorial Approach to the Full Vacuum Equations 230(7) L.J. Mason R. Penrose A Note on Causal Relations and Twistor Space 237(2) R. Low Towards a twistor description of general space-times Towards a Twistor Description of General Space-Times; Introductory Comments 239(17) R. Penrose Remarks on the Sparling and Eguchi-Hanson (Googly?) GravitionsR. Penrose 256(8) A New Angle on the Googly Graviton 264(6) R. Penrose Concerning a Fourier Contour Integral 270(1) R. Penrose The Googly Maps for the Eguchi-Hanson/Sparling-Tod Graviton 271(3) P.R. Law Physical Left-Right Symmetry and Googlies 274(6) R. Penrose On the Geometry of Googly Maps 280(3) R. Penrose P.R. Law A Prosaic Approach to Googlies 283(3) A. Helfer More on Googlies 286(3) A. Helfer A Note on Sparlings 3-Form 289(1) R. Penrose Remarks on Curved-Space Twistor Theory and Googlies 290(3) R. Penrose Relative Cohomology, Googlies and Deformations of II 293(2) R. Penrose Is the Plebanski Viewpoint Relevant to the Googly Problem? 295(8) G. Burnett-Stuart Note on the Geometry of the Googly Mappings 303(1) P.R. Law Exponentiating a Relative H2 304(2) R. Penrose The Complex Structure of Deformed Twistor Space 306(4) P.R. Law Local Twistor Transport at I+ : An Approach to the Googly 310(7) R. Penrose An Approach to a Coordinate Free Calculus at I 317(2) R. Penrose V. Thomas Twistor Theory for Vacuum Space-Time: A New Approach 319(5) R. Penrose Twistors as Charges for Spin 3/2 in Vacuum 324(6) R. Penrose Light Cone Cuts and Yang-Mills Holonomies: a New Approach 330(8) L.J. Manson Twistor as Spin 3/2 Charges Continued: SL(3, C) Bundles 338(7) R. Penrose The Most General (2,2) Self-Dual Vacuum: A Googly Approach 345(4) L. Haslehurst R. Penrose A Comment on the Preceding Article 349(4) N.M.J. Woodhouse Spin 3/2 Fields and Local Twistors 353(7) L.J. Mason R. Penrose Another View of the Spin 3/2 Equation 360(3) Jorg Frauendiener The Bach Equations as an Exact Set of Spinor Fields 363(4) Jorg Frauendiener A Novel Approach to Quantum Gravity 367(3) L.P. Hughston Twistor and the Time-Irreversibility of State-Vector Reduction 370(2) R. Penrose Twistors and State-Vector Reduction 372(3) R. Penrose Bibliography 375(28) Index 403
St Peters College and the Mathematical Institute, Oxford, Kings College London, Instytut Matematyki, Uniwersytet Jagielloski Kraków, Center for Mathematical Sciences, Munich University of Technology, Munich
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