Differential Geometry and Topology of Curves
eBook - ePub

Differential Geometry and Topology of Curves

  1. 216 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Differential Geometry and Topology of Curves

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 & Differential Equations. We have over one million books available in our catalogue for you to explore.

Information

Publisher
CRC Press
Year
2001
eBook ISBN
9781040199244
Edition
0
Topic
Mathematics
Subtopic
Differential Equations
Index
Mathematics

Table of contents

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