Geodesic
Some Invariants of Admissible Homotopies of Space Curves
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 54-66.

Voir la notice de l'article provenant de la source Math-Net.Ru

A regular homotopy of a generic curve in a three-dimensional projective space is called admissible if it defines a generic one-parameter family of curves in which every curve has neither self-intersections nor inflection points, is not tangent to a smooth part of its evolvent, and has no tangent planes osculating with the curve at two different points. We indicate some invariants of admissible homotopies of space curves and prove, in particular, that the curve $x=\cos t$, $y=\sin t$, $z=\cos 3t$ cannot be deformed in the class of admissible homotopies into a curve without flattening points. 
@article{FAA_2001_35_4_a6,
     author = {V. D. Sedykh},
     title = {Some {Invariants} of {Admissible} {Homotopies} of {Space} {Curves}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {54--66},
     publisher = {mathdoc},
     volume = {35},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a6/}
}
TY  - JOUR
AU  - V. D. Sedykh
TI  - Some Invariants of Admissible Homotopies of Space Curves
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2001
SP  - 54
EP  - 66
VL  - 35
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a6/
LA  - ru
ID  - FAA_2001_35_4_a6
ER  - 
%0 Journal Article
%A V. D. Sedykh
%T Some Invariants of Admissible Homotopies of Space Curves
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2001
%P 54-66
%V 35
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a6/
%G ru
%F FAA_2001_35_4_a6
V. D. Sedykh. Some Invariants of Admissible Homotopies of Space Curves. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 54-66. http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a6/

[1] Arnold V. I., “K lezhandrovoi teorii Shturma prostranstvennykh krivykh”, Funkts. analiz i ego pril., 32:2 (1998), 1–7 | DOI | MR | Zbl

[2] Arnold V. I., Zadachi Arnolda, Fazis, M., 2000 | MR

[3] Barner M., “Über die Mindestanzahl stationärer Schmiegebenen bei geschlossenen streng-konvexen Raumkurven”, Abh. Math. Sem. Univ. Hamburg, 20 (1956), 196–215 | DOI | MR | Zbl

[4] Vasilev V. A., Topologiya dopolnenii k diskriminantam, Fazis, M., 1997 | MR

[5] Sedykh V. D., “Stroenie vypukloi obolochki prostranstvennoi krivoi”, Trudy seminara Petrovskogo, 6, 1981, 239–256 | MR | Zbl

[6] Sedykh V. D., “Teorema o chetyrekh vershinakh vypukloi prostranstvennoi krivoi”, Funkts. analiz i ego pril., 26:1 (1992), 35–41 | MR | Zbl