Abstract:
We give an intrinsic definition of the special geometry which arises in global N= 2 supersymmetry in four dimensions. The base of an algebraic integrable system exhibits this geometry, and with an integrality hypothesis any special Kähler manifold is so related to an integrable system. The cotangent bundle of a special Kähler manifold carries a hyperkähler metric. We also define special geometry in supergravity in terms of the special geometry in global supersymmetry.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 5 December 1997 / Accepted: 16 November 1998
Rights and permissions
About this article
Cite this article
Freed, D. Special Kähler Manifolds. Comm Math Phys 203, 31–52 (1999). https://doi.org/10.1007/s002200050604
Issue Date:
DOI: https://doi.org/10.1007/s002200050604