Flat approximations of hypersurfaces along curves

Irina Markina, Matteo Raffaelli*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Given a smooth curve γ in some m-dimensional surface M in Rm + 1, we study existence and uniqueness of a flat surface H having the same field of normal vectors as M along γ, which we call a flat approximation of M along γ. In particular, the well-known characterisation of flat surfaces as torses (ruled surfaces with tangent plane stable along the rulings) allows us to give an explicit parametric construction of such approximation.

Original languageEnglish
JournalManuscripta Mathematica
Volume160
Issue number3-4
Pages (from-to)315-325
Number of pages11
ISSN0025-2611
DOIs
Publication statusPublished - 2019

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