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 language | English |
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Journal | Manuscripta Mathematica |
Volume | 160 |
Issue number | 3-4 |
Pages (from-to) | 315-325 |
Number of pages | 11 |
ISSN | 0025-2611 |
DOIs | |
Publication status | Published - 2019 |