**Observations 11:**


The soldering of the principal frame bundle allows us to define the torsion form<sup>20</sup> .

**Definition 20** (Torsion form)**.** *Let P* = *FO*(*M*)*, ρ* : *O*(3, 1) → Aut(*V*) *be the fundamental representation, V be a vector space with reference metric <sup>η</sup>, and <sup>θ</sup>* <sup>∈</sup> <sup>Ω</sup><sup>1</sup> *G* (*P*, *V*) *be a solder form. We define the torsion form* <sup>Θ</sup> <sup>∈</sup> <sup>Ω</sup><sup>2</sup> *G* (*P*, *V*) *as follows:*

$$
\Theta = d\_{\omega}\theta = d\theta + \omega \wedge\_f \theta. \tag{54}
$$
