Pontryagin and Euler forms and Chern-Simons terms in Weyl-Cartan space

TL;DR

This paper establishes the existence of Pontryagin and Euler forms in Weyl-Cartan space using variational methods and shows they can be expressed through Chern-Simons terms, highlighting their geometric and topological significance.

Contribution

It demonstrates the existence of Pontryagin and Euler forms in Weyl-Cartan space and relates them to Chern-Simons terms, extending geometric understanding in this context.

Findings

Pontryagin and Euler forms exist in Weyl-Cartan space.

These forms can be expressed as exterior derivatives of Chern-Simons terms.

The results incorporate torsion and nonmetricity in the geometric framework.

Abstract

The existence of the Pontryagin and Euler forms in a Weyl-Cartan space on the basis of the variational method with Lagrange multipliers are established. It is proved that these forms can be expressed via the exterior derivatives of the corresponding Chern-Simons terms in a Weyl-Cartan space with torsion and nonmetricity.