I would like to see why here it cannot be globally the case $E=B\times F$ and $\pi$ for the porjection in the hairbrush case ? Also what corresponds to $h,p,\tilde{h}_0$ in hairbrush.
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Does this help? – student91 Feb 23 '23 at 12:13
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the page you linked to does not mention a hairbrush. What is "the hairbrush case"? – student91 Feb 23 '23 at 12:14