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:
File Dimensione Formato  
Gauss.pdf

solo utenti autorizzati

Tipologia: Versione Editoriale (PDF)
Licenza: Non pubblico
Dimensione 341.38 kB
Formato Adobe PDF
341.38 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
1504.02739.pdf

accesso aperto

Descrizione: https://arxiv.org/pdf/1504.02739.pdf
Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 193.86 kB
Formato Adobe PDF
193.86 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1069264
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 6
social impact