latex_formula: \[v\cdot f^{*}A|_{x}=(f\lrcorner Z)_{*}v\cdot A|_{f\lrcorner Z(x)},\quad x\in Z, \ v\in T_{x}Z.\]


latex_formula: \[(f\lrcorner Z)_{*}v\cdot A|_{f\lrcorner Z(x)}=v^{\alpha\dot{\alpha}}\Big{(} \frac{\partial y^{\beta\dot{\beta}}}{\partial x^{\alpha\dot{\alpha}}}A_{\beta \dot{\beta}}\Big{)}\Big{|}_{f\lrcorner Z(x)},\ x\in Z,\ v\in T_{x}Z,\]


latex_formula: \[f\lrcorner L(z)=\pi_{1}\circ f(z,\lambda,\tilde{\lambda})\ \forall z\in L\]