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 / Pietro De, Poi; Ilardi, Giovanna. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 219:11(2015), pp. 5137-5148.
On higher Gauss maps
ILARDI, GIOVANNA
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.File in questo prodotto:
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