*4.2. For a Connection Form ω*

**Definition 16** (*dω*)**.** *Let <sup>P</sup> be a G-principal bundle, <sup>V</sup> be a vector space, and <sup>α</sup>* <sup>∈</sup> <sup>Ω</sup>*<sup>k</sup> G* (*P*, *V*) *be a tensorial form. We define the exterior covariant derivative d<sup>ω</sup> as a map d<sup>ω</sup>* : Ω*<sup>k</sup> G* (*P*, *<sup>V</sup>*) <sup>→</sup> <sup>Ω</sup>*k*+<sup>1</sup> *G* (*P*, *V*) *such that*<sup>13</sup>

$$\begin{array}{rcl}d\,\_{\omega}\mathfrak{a} &:= d\mathfrak{a} + \omega \wedge\_{d\rho} \mathfrak{a} \\ &:= d\mathfrak{a} + d\rho \circ \omega \wedge \mathfrak{a}.\end{array} \tag{27}$$
