Pontryagin, Euler Forms and Chern–Simons Terms in Weyl–Cartan Space

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.