ScalingStacks

Lemma 4.5 . [044R]

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Lemma 4.5.

The following integrability condition is satisfied globally

∂wp​q¯∂ηr=∂wr​q∂ηp,∂wp​q¯∂η¯r=∂wp​r∂η¯q,p,q,r=1,2.\frac{\partial w^{p\bar{q}}}{\partial\eta_{r}}=\frac{\partial w^{rq}}{\partial\eta_{p}},\quad\frac{\partial w^{p\bar{q}}}{\partial\bar{\eta}_{r}}=\frac{\partial w^{pr}}{\partial\bar{\eta}_{q}},\quad p,q,r=1,2.

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