Differential Geometry and Topology of Curves
eBook - PDF

Differential Geometry and Topology of Curves

  1. 216 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Differential Geometry and Topology of Curves

Book details
Table of contents
Citations

About This Book

Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditi

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Yes, you can access Differential Geometry and Topology of Curves by Yu Animov in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher
CRC Press
Year
2001
ISBN
9781420022605
Edition
1
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Front Cover
  2. Contents
  3. Preface
  4. Chapter 1: Definition of a Curve
  5. Chapter 2: Vector-valued Functions Depending on Numerical Arguments
  6. Chapter 3: The Regular Curve and its Representations
  7. Chapter 4: Straight Line Tangent to a Curve
  8. Chapter 5: Osculating Plane of a Curve
  9. Chapter 6: The Arc Length of a Curve
  10. Chapter 7: The Curvature and Torsion of a Curve
  11. Chapter 8: Osculating Circle of a Plane Curve
  12. Chapter 9: Singular Points of Plane Curves
  13. Chapter 10: Peano's Curve
  14. Chapter 11: Envelope of the Family of Curves
  15. Chapter 12: Frenet Formulas
  16. Chapter 13: Determination of a Curve with Given Curvature and Torsion
  17. Chapter 14: Analogies of Curvature and Torsion for Polygonal Lines
  18. Chapter 15: Curves with a Constant Ratio of Curvature and Torsion
  19. Chapter 16: Osculating Sphere
  20. Chapter 17: Special Planar Curves
  21. Chapter 18: Curves in Mechanics
  22. Chapter 19: Curve Filling a Surface
  23. Chapter 20: Curves with Locally Convex Projection
  24. Chapter 21: Integral Inequalities for Closed Curves
  25. Chapter 22: Reconstruction of a Closed Curve with Given Spherical Indicatrix of Tangents
  26. Chapter 23: Conditions for a Curve to be Closed
  27. Chapter 24: Isoperimetric Property of a Circle
  28. Chapter 25: One Inequality for a Closed Curve
  29. Chapter 26: Necessary and Sufficient Condition of the Boundedness of a Curve with Periodic Curvature and Torsion
  30. Chapter 27: Delaunay's Problem
  31. Chapter 28: Jordan's Theorem on Closed Plane Curves
  32. Chapter 29: Gauss's Integral for Two Linked Curves
  33. Chapter 30: Knots
  34. Chapter 31: Alexander's Polynomial
  35. Chapter 32: Curves in n-dimensional Euclidean Space
  36. Chapter 33: Curves with Constant Curvatures in n-dimensional Euclidean Space
  37. Chapter 34: Generalization of the Fenchel Inequality
  38. Chapter 35: Knots and Links in Biology and One Mystery
  39. Chapter 36: Jones' Polynomial, Its Generalization and Some Applications
  40. References
  41. Index
  42. Back Cover