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Handbook of Pseudo-Riemannian Geometry and Supersymmetry
IRMA Lectures in Mathematics and Theoretical Physics Vol. 16

Handbook of Pseudo-Riemannian Geometry and Supersymmetry

Vicente Cortés

ISBN print 978-3-03719-079-1, ISBN online 978-3-03719-579-6
DOI 10.4171/079
June 2010, 964 pages, hardcover, 17 x 24 cm.
118.00 Euro

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.

    Keywords: Pseudo-Riemannian manifold, supersymmetry, special geometry, quaternionic Kähler manifold, c-map, generalized geometry, sigma-model, skew-symmetric torsion, nearly Kähler manifold, Euclidian supersymmetry, black hole, para-geometries

    Further Information

    Review in MR 2605651 (2011c:53001)