The Einstein 3-form Gα and its equivalent 1-form Lα in Riemann-Cartan space

Abstract

The definition of the Einstein 3-form Gα is motivated by means of the contracted 2nd Bianchi identity. This definition involves at first the complete curvature 2-form. The 1-form Lα is defined via Gα = L β ∧ ⋆ (ϑβ ∧ ϑα) (here ⋆ is the Hodge-star, ϑα the coframe). It is equivalent to the Einstein 3-form and represents a certain contraction of the curvature 2-form. A variational formula of Salgado on quadratic invariants of the Lα 1-form is discussed, generalized, and put into proper perspective. 1