We prove that the general fibre of the i-th Gauss map has dimension m if and only if at the general point the (i+1)-th fundamental form consists of cones with vertex a fixed P^(m−1), extending a known theorem for the usual Gauss map. We prove this via a recursive formula for expressing higher fundamental forms. We also show some consequences of these results.
On higher Gauss maps
DE POI, Pietro;
2015-01-01
Abstract
We prove that the general fibre of the i-th Gauss map has dimension m if and only if at the general point the (i+1)-th fundamental form consists of cones with vertex a fixed P^(m−1), extending a known theorem for the usual Gauss map. We prove this via a recursive formula for expressing higher fundamental forms. We also show some consequences of these results.File in questo prodotto:
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Gauss.pdf
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1504.02739.pdf
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Descrizione: https://arxiv.org/pdf/1504.02739.pdf
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