Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 54-66
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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/
@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},
year = {2001},
volume = {35},
number = {4},
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
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
%U http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a6/
%G ru
%F FAA_2001_35_4_a6
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.
