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Handbook of Pseudo-Riemannian Geometry and Supersymmetry

Vicente Cortés, editor
European Mathematical Society
Publication Date: 
Number of Pages: 
IRMA Lectures in Mathematics and Theoretical Physics 16
We do not plan to review this book.

Part A. Special geometry and supersymmetry

  • M. Roček, C. Vafa, and S. Vandoren -- Quaternion-Kähler spaces, hyper-Kähler cones, and the c-map geometry
  • G. Weingart -- Differential forms on quaternionic Kähler manifolds
  • C. P. Boyer and K. Galicki -- Sasakian geometry, holonomy, and supersymmetry
  • M. A. Lledó, O. Maciá, A. Van Proeyen, and V. S. Varadarajan -- Special geometry for arbitrary signatures
  • T. Mohaupt -- Special geometry, black holes and Euclidean supersymmetry

Part B. Generalized geometry

  • N. Hitchin -- Generalized geometry--an introduction
  • A. Kotov and T. Strobl -- Generalizing geometry--algebroids and sigma models
  • U. Lindström, M. Roček, R. von Unge, and M. Zabzine -- A potential for generalized Kähler geometry

Part C. Geometries with torsion

  • I. Agricola -- Non-integrable geometries, torsion, and holonomy
  • P.-A. Nagy -- Totally skew-symmetric torsion and nearly-Kähler geometry
  • J.-B. Butruille -- Homogeneous nearly Kähler manifolds
  • L. Schäfer and F. Schulte-Hengesbach -- Nearly pseudo-Kähler and nearly para-Kähler six-manifolds
  • A. Swann -- Quaternionic geometries from superconformal symmetry

Part D. Para-geometries

  • S. Ivanov, I. Minchev, and S. Zamkovoy -- Twistor and reflector spaces of almost para-quaternionic manifolds
  • M. Krahe -- Para-pluriharmonic maps and twistor spaces
  • D. V. Alekseevsky, C. Medori, and A. Tomassini -- Maximally homogeneous para-CR manifolds of semisimple type

Part E. Holonomy theory

  • A. Galaev and T. Leistner -- Recent developments in pseudo-Riemannian holonomy theory
  • A. J. Di Scala, T. Leistner, and T. Neukirchner -- Geometric applications of irreducible representations of Lie groups
  • K. Waldorf -- Surface holonomy

Part F. Symmetric spaces and spaces of constant curvature theory

  • I. Kath -- Classification results for pseudo-Riemannian symmetric spaces
  • D. V. Alekseevsky -- Pseudo-Kähler and para-Kähler symmetric spaces
  • O. Baues -- Prehomogeneous affine representations and flat pseudo-Riemannian manifolds

Part G. Conformal geometry

  • H. Baum -- The conformal analog of Calabi-Yau manifolds
  • Y. Kamishima -- Nondegenerate conformal structures, CR structures and quaternionic CR structures on manifolds

Part H. Other topics of recent interest

  • C. Bär -- Linear wave equations on Lorentzian manifolds
  • D. S. Freed -- Survey of D-branes and K-theory
  • List of contributors
  • Index