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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1069264
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