Handbook of Pseudo-Riemannian Geometry and Supersymmetry

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