Deformations of classical geometries and integrable systems

Abstract

A generalization of the notion of a (pseudo-) Riemannian space is proposed in a framework of noncommutative geometry. In particular, there are parametrized families of generalized Riemannian spaces which are deformations of classical geometries. We also introduce harmonic maps on generalized Riemannian spaces into Hopf algebras and make contact with integrable models in two dimensions.

14 pages, LaTeX

References in corpus (1)

• Some aspects of noncommutative geometry and physics

Cited by in corpus (2)

• Discrete Riemannian Geometry
• The Generalized Moyal Nahm and Continuous Moyal Toda Equations