Journal article · Preprint article
Flat approximations of hypersurfaces along curves
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.
Language: | English |
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Publisher: | Springer Berlin Heidelberg |
Year: | 2019 |
Pages: | 315-325 |
ISSN: | 14321785 and 00252611 |
Types: | Journal article and Preprint article |
DOI: | 10.1007/s00229-018-1072-6 |
ORCIDs: | 0000-0002-4908-196X |