Cortés Vicente (ed.) Handbook of Pseudo-Riemannian Geometry and Supersymmetry

European Mathematical Society, 2010. — 964 p. — (IRMA Lectures in Mathematics and Theoretical Physics 16). — ISBN: 978-3-03719-079-1.The project for this special volume on pseudo-Riemannian geometry and supersymmetry grew out of the 77th “Encounter between Mathematicians and Theoretical Physicists” at the Institut de Recherche Mathématique Avancée in Strasbourg in 2005.
A number of authors of this volume participated in that meeting, including our friend Kris Galicki, who died as a consequence of a tragic hiking accident in 2007. He was always interested in the differential geometric structures occurring in physical theories and was one of the rare scientists who mastered the language of mathematics as well as that of physics.Special geometry and supersymmetry
Quaternion-Kähler spaces, hyper-Kähler cones, and the c-map
Differential forms on quaternionic Kähler manifolds
Sasakian geometry, holonomy, and supersymmetry
Special geometry for arbitrary signatures
Special geometry, black holes and Euclidean supersymmetry
Generalized geometry
Generalized geometry – an introduction
Generalizing geometry – algebroids and sigma models
A potential for generalized Kähler geometry
Geometries with torsion
Non-integrable geometries, torsion, and holonomy
Connections with totally skew-symmetric torsion and nearly-Kähler geometry
Homogeneous nearly Kähler manifolds
Nearly pseudo-Kähler and nearly para-Kähler six-manifolds
Quaternionic geometries from superconformal symmetry
Para-geometries
Twistor and reflector spaces of almost para-quaternionic manifolds
Para-pluriharmonic maps and twistor spaces
Maximally homogeneous para-CR manifolds of semisimple type
Holonomy theory
Recent developments in pseudo-Riemannian holonomy theory
Geometric applications of irreducible representations of Lie groups
Surface holonomy
Symmetric spaces and spaces of constant curvature
Classification results for pseudo-Riemannian symmetric spaces
Pseudo-Kähler and para-Kähler symmetric spaces
Prehomogeneous affine representations and flat pseudo-Riemannian manifolds
Conformal geometry
The conformal analog of Calabi–Yau manifolds
Nondegenerate conformal structures, CR structures and quaternionic CR structures on manifolds
Other topics of recent interest
Linear wave equations on Lorentzian manifolds
Survey of D-branes and K-theory