1st Edition

Further Advances in Twistor Theory, Volume III Curved Twistor Spaces

Edited By L.J. Mason, P.Z. Kobak, L. Hughston, K. Pulverer Copyright 2001
    432 Pages 50 B/W Illustrations
    by Chapman & Hall

    432 Pages
    by Chapman & Hall

    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.

    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
    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
    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; 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


    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

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