Flat approximations of hypersurfaces along curves
Abstract
Given a smooth curve $\gamma$ in some $m$dimensional surface $M$ in $\mathbb{R}^{m+1}$, we study existence and uniqueness of a flat surface $H$ having the same field of normal vectors as $M$ along $\gamma$, which we call a flat approximation of $M$ along $\gamma$. In particular, the wellknown 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2018
 DOI:
 10.48550/arXiv.1812.00826
 arXiv:
 arXiv:1812.00826
 Bibcode:
 2018arXiv181200826M
 Keywords:

 Mathematics  Differential Geometry;
 53A07 (Primary) 53B20 (Secondary)
 EPrint:
 11 pages, no figures