A curvature identity on a 6-dimensional Riemannian Manifold and its applications

TL;DR

This paper derives a new curvature identity specific to 6-dimensional Riemannian manifolds from the Chern-Gauss-Bonnet theorem and explores its applications.

Contribution

It introduces a novel curvature identity for 6D Riemannian manifolds and demonstrates its applications.

Findings

Derived a curvature identity for 6D Riemannian manifolds.

Established applications of the curvature identity.

Connected the identity to the Chern-Gauss-Bonnet theorem.

Abstract

We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. We also introduce some applications of this curvature identity.