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

TL;DR

This paper derives general formulas for the coefficients of Chern forms up to the 13th order in curvature, expressed through the Riemann-Christoffel tensor and related tensors, applicable to n-dimensional manifolds with linear connections.

Contribution

It provides explicit general expressions for Chern form coefficients up to the 13th order, expanding the computational tools for differential geometry.

Findings

Formulas for Chern form coefficients up to 13th order

Expressions involve Riemann-Christoffel curvature tensor and concomitants

Applicable to n-dimensional manifolds with general linear connections

Abstract

General expressions are given for the coefficients of Chern forms up to the 13th order in curvature in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for n-dimensional differentiable manifolds having a general linear connection.