Differential geometry and topology of curves / Yu Aminov.

Includes bibliographical references (p. 199-202) and index.

1. Definition of a curve -- 2. Vector-valued functions depending on numerical arguments -- 3. The regular curve and its representations -- 4. Straight line tangent to a curve -- 5. Osculating plane of a curve -- 6. The arc length of a curve -- 7. The curvature and torsion of a curve -- 8. Osculating circle of a plane curve -- 9. Singular points of plane curves -- 10. Peano's curve -- 11. Envelope of the family of curves -- 12. Frenet formulas -- 13. Determination of a curve with given curvature and torsion -- 14. Analogies of curvature and torsion for polygonal lines -- 15. Curves with a constant ratio of curvature and torsion -- 16. Osculating sphere -- 17. Special planar curves -- 18. Curves in mechanics -- 19. Curve filling a surface -- 20. Curves with locally convex projection -- 21. Integral inequalities for closed curves -- 22. Reconstruction of a closed curve with given spherical indicatrix of tangents -- 23. Conditions for a curve to be closed -- 24. Isoperimetric property of a circle -- 25. One inequality for a closed curve -- 26. Necessary and sufficient condition of the boundedness of a curve with periodic curvature and torsion -- 27. Delaunay's problem -- 28. Jordan's theorem on closed plane curves -- 29. Gauss's integral for two linked curves -- 30. Knots -- 31. Alexander's polynomial -- 32. Curves in n-dimensional Euclidean space -- 33. Curves with constant curvatures in n-dimensional Euclidean space -- 34. Generalization of the Fenchel inequality -- 35. Knots and links in biology and one mystery -- 36. Jones' polynomial, its generalization and some applications.

Also available as an electronic resource.