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 IRMA Lectures in Mathematics and Theoretical Physics 2010; 964 pp; hardcover Volume: 16 ISBN-10: 3-03719-079-5 ISBN-13: 978-3-03719-079-1 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 Para-geometries Holonomy theory Symmetric spaces and spaces of constant curvature Conformal geometry Wave equations on Lorentzian manifolds D-branes and K-theory 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 pseudo-Riemannian 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 -- 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