Geodesic
Local Singularities of Chord Sets
Matematičeskie zametki, Tome 83 (2008) no. 2, pp. 286-304 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the present paper, we classify the local singularities of chord sets, i.e., of the envelopes of two-parameter families of straight lines connecting pairs of points on two smooth curves in $\mathbb R^3$; we also present geometric criteria for the chord set to have a given local singularity.
Keywords: smooth curves in $\mathbb R^3$, chord set, local singularity, smooth curve, germ of a curve, diffeomorphism, projective invariance. 
@article{MZM_2008_83_2_a9,
     author = {L. P. Stunzhas},
     title = {Local {Singularities} of {Chord} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {286--304},
     year = {2008},
     volume = {83},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_2_a9/}
}
TY  - JOUR
AU  - L. P. Stunzhas
TI  - Local Singularities of Chord Sets
JO  - Matematičeskie zametki
PY  - 2008
SP  - 286
EP  - 304
VL  - 83
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_83_2_a9/
LA  - ru
ID  - MZM_2008_83_2_a9
ER  - 
%0 Journal Article
%A L. P. Stunzhas
%T Local Singularities of Chord Sets
%J Matematičeskie zametki
%D 2008
%P 286-304
%V 83
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2008_83_2_a9/
%G ru
%F MZM_2008_83_2_a9
L. P. Stunzhas. Local Singularities of Chord Sets. Matematičeskie zametki, Tome 83 (2008) no. 2, pp. 286-304. http://geodesic.mathdoc.fr/item/MZM_2008_83_2_a9/

[1] V. I. Arnold, A. N. Varchenko, S. M. Gusein-Zade, Osobennosti differentsiruemykh otobrazhenii, Izd-vo MTsNMO, M., 2004 | MR | MR | Zbl

[2] Sh. Izumiya, N. Takeuchi, “Singularities of ruled surfaces in $\mathbb R^3$”, Turkish J. Math., 28:2 (2004), 153–163 ; http://eprints.math.sci.hokudai.ac.jp/archive/00000648/ | MR | Zbl

[3] Dzh. N. Mazer, “Ustoichivost $C^\infty$-otobrazhenii. V. Transversalnost”, UMN, 29:1 (1974), 99–128 | MR | Zbl