Processing math: 100%

#	Differential Forms
#	Physical Object	N-dimensional form	Locally Expression in $M .$
1	Deformed Line	1-form: $l (= δ z)$	$δ z = I_{α β} Z^{α} d Z^{β} = \in^{A^{'} B^{'}} π_{A^{'}} π_{B^{'}}$
2	2-Dimensional Waving Space (for example Figure 4(b)))	2-form: $τ = \frac{1}{2} d L$	$τ = \frac{1}{2} I_{α β} d Z^{α} \land d Z^{β} = \in^{A^{'} B^{'}} d π_{A^{'}} \land d π_{B^{'}}$
	$H$ -Spaae	3-form: $θ$	$\begin{matrix} θ = \frac{1}{6} \in_{α β γ δ} Z^{α} d Z^{β} \land d Z^{γ} \land d Z^{δ} \\ = Z^{0} d Z^{1} \land d Z^{2} \land d Z^{3} - Z^{1} d Z^{0} \land d Z^{2} \land d Z^{3} \\ + Z^{2} d Z^{0} \land d Z^{1} \land d Z^{3} - Z^{3} d Z^{0} \land d Z^{1} \land d Z^{2} \end{matrix}$
4	Spin Bundle	4-form: $ϕ = \frac{1}{4} d θ$	$\begin{matrix} ϕ = \frac{1}{24} \in_{α β γ δ} d Z^{α} \land d Z^{β} \land d Z^{γ} \land d Z^{δ} \\ = d Z^{0} \land d Z^{1} \land d Z^{2} \land d Z^{3} \end{matrix}$
5	Field Distorsion Components	Euler form: $Υ = θ : ϕ,$ Math_170#	$Υ = Z^{α} \frac{\partial}{\partial Z^{α}}$