Flat approximations of hypersurfaces along curves

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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
Number of pages11
Publication statusAccepted/In press - 2019
CitationsWeb of Science® Times Cited: No match on DOI

ID: 188455068