Differential geometry and topology of curves /
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton :
CRC Press,
2000.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- 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.