General Expressions for Chern Forms Up to the 13th Order in Curvature

TL;DR

This paper derives general polynomial expressions for Chern forms up to the 13th order in curvature, applicable to n-dimensional manifolds with a general linear connection, advancing the mathematical understanding of characteristic classes.

Contribution

It provides explicit formulas for high-order Chern forms in terms of curvature polynomials, extending previous results to the 13th order.

Findings

Explicit formulas for Chern forms up to the 13th order.

Expressions in terms of polynomial concomitants of curvature.

Applicable to n-dimensional manifolds with general linear connections.

Abstract

General expressions are given for Chern forms up to the 13th order in curvature in terms of simple polynomial concomitants of the curvature 2-form for n-dimensional differentiable manifolds having a general linear connection.