Piani e sfere osculatrici ad archi differenziabili
Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 111-124
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The existence of osculating planes is established for a large class of differentiable arcs in $\mathbb{R}_{n}$, called "coherent"; all analytic arcs, including the singular ones, belong to this family. On a coherent arc, osculating planes and spheres exist at any point and vary differentiably; Frenet formulas and curvatures are reformulated in order to generalize the classical ones. Coherent arcs form an open set in the space of all arcs, with infinite codimensional complement.
Lazzeri, F. Piani e sfere osculatrici ad archi differenziabili. Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 111-124. http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a3/
@article{BUMI_2010_9_3_1_a3,
author = {Lazzeri, F.},
title = {Piani e sfere osculatrici ad archi differenziabili},
journal = {Bollettino della Unione matematica italiana},
pages = {111--124},
year = {2010},
volume = {Ser. 9, 3},
number = {1},
zbl = {1192.53006},
mrnumber = {2605914},
language = {it},
url = {http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a3/}
}