论文信息 - On closed twisted curves

On closed twisted curves

Twisted curves in R'" are those which have independent derivatives up to order m . For plane and spatial curves the twisted condition is equivalent to never vanishing curvature and torsion respectively. We give a necessary and sufficient condition for a (q, p)-curve on a torus to be twisted, and use those curves to construct closed twisted curves in R'? for all m .

S. Costa

[1] Über reelle geschlossene Raumkurven vierter Ordnung , 1936 .

[2] W. Fenchel,et al. On the differential geometry of closed space curves , 1951 .

[3] Über die Mindestanzahl stationärer Schmiegebenen bei geschlossenen streng-konvexen Raumkurven , 1956 .

[4] William Francis Pohl,et al. Differential geometry of higher order , 1962 .

[5] E. Feldman. The geometry of immersions. I , 1963 .

[6] Herman Gluck,et al. Higher Curvatures of Curves in Euclidean Space, II , 1966 .

[7] E. Feldman. Deformations of closed space curves , 1968 .

[8] W. Pohl. Singularities in the differential geometry of submanifolds , 1971 .

[9] J. Little. Third order nondegenerate homotopies of space curves , 1971 .

[10] A generalization of the two-vertex theorem for space curves , 1975 .

[11] Closed curves of constant torsion. II , 1977 .

[12] J. Little. Space curves with positive torsion , 1978 .

[13] Michael H. Freedman,et al. Planes triply tangent to curves with nonvanishing torsion , 1980 .

[14] Inflectional Convex Space Curves , 1984, Canadian Journal of Mathematics.

[15] Convexly generic curves in R3 , 1988 .

[16] M. Fuster. Convexly generic curves in R 3 , 1988 .