Some Invariants of Admissible Homotopies of Space Curves

V. D. Sedykh

Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 54-66

Résumé

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.