Exact formulas for the approximation of connections and curvature

Abstract

First we express the holonomy along a boundary curve as the integral on the domain, of an expression which is linear in the curvature. Then we provide a rigorous justification of the definition of curvature in Regge calculus.

15 pages. v2 extends the justification of Regge calculus from two to arbitrary dimensions

References in corpus (3)

• Simplicial Ricci Flow
• Analysis of curvature approximations via covariant curl and incompatibility for Regge metrics
• Finite element approximation of scalar curvature in arbitrary dimension

Cited by in corpus (2)

• Blow-up Whitney forms, shadow forms, and Poisson processes
• On the improved convergence of lifted distributional Gauss curvature from Regge elements