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.
Titolo: | On higher Gauss maps |
Autori: | |
Data di pubblicazione: | 2015 |
Rivista: | |
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. |
Handle: | http://hdl.handle.net/11390/1069264 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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