Pseudo-Riemannian Metrics in Models Based on Noncommutative Geometry

Abstract

Several examples and models based on noncommutative differential calculi on commutative algebras indicate that a metric should be regarded as an element of the left-linear tensor product of the space of 1-forms with itself. We show how the metric compatibility condition with a linear connection generalizes to this framework.

7 pages, contribution to 8th Colloquium on Quantum Groups and Integrable Systems, Prague, June 1999

References in corpus (2)

• Discrete Riemannian Geometry
• Noncommutative geometry and a class of completely integrable models

Cited by in corpus (1)

• Noncommutative Geometries and Gravity