Handbook of Pseudo-Riemannian Geometry and Supersymmetry [electronic resource] /
Vicente Cortés
- Zuerich, Switzerland : European Mathematical Society Publishing House, 2010
- 1 online resource (964 pages)
- IRMA Lectures in Mathematics and Theoretical Physics (IRMA) 16 .
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 – an introduction / Generalizing geometry – algebroids and sigma models / A potential for generalized Kähler geometry / 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 / Twistor and reflector spaces of almost para-quaternionic manifolds / Para-pluriharmonic maps and twistor spaces / Maximally homogeneous para-CR manifolds of semisimple type / Recent developments in pseudo-Riemannian holonomy theory / Geometric applications of irreducible representations of Lie groups / Surface holonomy / Classification results for pseudo-Riemannian symmetric spaces / Pseudo-Kähler and para-Kähler symmetric spaces / Prehomogeneous affine representations and flat pseudo-Riemannian manifolds / The conformal analog of Calabi–Yau manifolds / Nondegenerate conformal structures, CR structures and quaternionic CR structures on manifolds / Linear wave equations on Lorentzian manifolds / Survey of D-branes and K-theory / Martin Roček, Cumrun Vafa, Stefan Vandoren -- Gregor Weingart -- Charles P. Boyer, Krzysztof Galicki† -- María A. Lledó, Óscar Maciá, Antoine Van Proeyen, Veeravalli S. Varadarajan -- Thomas Mohaupt -- Nigel Hitchin -- Alexei Kotov, Thomas Strobl -- Ulf Lindström, Martin Roček, Rikard von Unge, Maxim Zabzine -- Ilka Agricola -- Paul-Andi Nagy -- Jean-Baptiste Butruille -- Lars Schäfer, Fabian Schulte-Hengesbach -- Andrew Swann -- Stefan Ivanov, Ivan Minchev, Simeon Zamkovoy -- Matthias Krahe -- Dmitri V. Alekseevsky, Costantino Medori, Adriano Tomassini -- Anton Galaev, Thomas Leistner -- Antonio J. Di Scala, Thomas Leistner, Thomas Neukirchner -- Konrad Waldorf -- Ines Kath -- Dmitri V. Alekseevsky -- Oliver Baues -- Helga Baum -- Yoshinobu Kamishima -- Christian Bär -- Daniel S. Freed.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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.
9783037195796
10.4171/079 doi
Differential & Riemannian geometry
Differential geometry
Quantum theory
Relativity and gravitational theory
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 – an introduction / Generalizing geometry – algebroids and sigma models / A potential for generalized Kähler geometry / 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 / Twistor and reflector spaces of almost para-quaternionic manifolds / Para-pluriharmonic maps and twistor spaces / Maximally homogeneous para-CR manifolds of semisimple type / Recent developments in pseudo-Riemannian holonomy theory / Geometric applications of irreducible representations of Lie groups / Surface holonomy / Classification results for pseudo-Riemannian symmetric spaces / Pseudo-Kähler and para-Kähler symmetric spaces / Prehomogeneous affine representations and flat pseudo-Riemannian manifolds / The conformal analog of Calabi–Yau manifolds / Nondegenerate conformal structures, CR structures and quaternionic CR structures on manifolds / Linear wave equations on Lorentzian manifolds / Survey of D-branes and K-theory / Martin Roček, Cumrun Vafa, Stefan Vandoren -- Gregor Weingart -- Charles P. Boyer, Krzysztof Galicki† -- María A. Lledó, Óscar Maciá, Antoine Van Proeyen, Veeravalli S. Varadarajan -- Thomas Mohaupt -- Nigel Hitchin -- Alexei Kotov, Thomas Strobl -- Ulf Lindström, Martin Roček, Rikard von Unge, Maxim Zabzine -- Ilka Agricola -- Paul-Andi Nagy -- Jean-Baptiste Butruille -- Lars Schäfer, Fabian Schulte-Hengesbach -- Andrew Swann -- Stefan Ivanov, Ivan Minchev, Simeon Zamkovoy -- Matthias Krahe -- Dmitri V. Alekseevsky, Costantino Medori, Adriano Tomassini -- Anton Galaev, Thomas Leistner -- Antonio J. Di Scala, Thomas Leistner, Thomas Neukirchner -- Konrad Waldorf -- Ines Kath -- Dmitri V. Alekseevsky -- Oliver Baues -- Helga Baum -- Yoshinobu Kamishima -- Christian Bär -- Daniel S. Freed.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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.
9783037195796
10.4171/079 doi
Differential & Riemannian geometry
Differential geometry
Quantum theory
Relativity and gravitational theory