IRMA Lectures in Mathematics and Theoretical Physics 2010; 964 pp; hardcover Volume: 16 ISBN10: 3037190795 ISBN13: 9783037190791 List Price: US$138 Member Price: US$110.40 Order Code: EMSILMTP/16
 The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are:  Special geometry and supersymmetry
 Generalized geometry
 Geometries with torsion
 Parageometries
 Holonomy theory
 Symmetric spaces and spaces of constant curvature
 Conformal geometry
 Wave equations on Lorentzian manifolds
 Dbranes and Ktheory
The intended audience consists of advanced students and researchers working in differential geometry, string theory, and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudoRiemannian geometry. Others lead to new concepts relating various fields of research, such as special Kähler geometry or generalized geometry. A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in differential geometry, string theory, and related areas. Table of Contents Part A. Special geometry and supersymmetry  M. Roček, C. Vafa, and S. Vandoren  QuaternionKähler spaces, hyperKähler cones, and the cmap 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 geometryan introduction
 A. Kotov and T. Strobl  Generalizing geometryalgebroids 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  Nonintegrable geometries, torsion, and holonomy
 P.A. Nagy  Totally skewsymmetric torsion and nearlyKähler geometry
 J.B. Butruille  Homogeneous nearly Kähler manifolds
 L. Schäfer and F. SchulteHengesbach  Nearly pseudoKähler and nearly paraKähler sixmanifolds
 A. Swann  Quaternionic geometries from superconformal symmetry
Part D. Parageometries  S. Ivanov, I. Minchev, and S. Zamkovoy  Twistor and reflector spaces of almost paraquaternionic manifolds
 M. Krahe  Parapluriharmonic maps and twistor spaces
 D. V. Alekseevsky, C. Medori, and A. Tomassini  Maximally homogeneous paraCR manifolds of semisimple type
Part E. Holonomy theory  A. Galaev and T. Leistner  Recent developments in pseudoRiemannian 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 pseudoRiemannian symmetric spaces
 D. V. Alekseevsky  PseudoKähler and paraKähler symmetric spaces
 O. Baues  Prehomogeneous affine representations and flat pseudoRiemannian manifolds
Part G. Conformal geometry  H. Baum  The conformal analog of CalabiYau 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 Dbranes and Ktheory
 List of contributors
 Index
