Differential Geometry and Topology of Curves

by ;
Format: Hardcover
Pub. Date: 2001-01-11
Publisher(s): CRC Press
  • Free Shipping Icon

    Free Shipping on all Orders Over $35!*

    *excludes Marketplace items.

List Price: $185.00

Buy New

Usually Ships in 5-7 Business Days

Rent Textbook

Select for Price
There was a problem. Please try again later.

Rent Digital

Online: 180 Days access
Downloadable: 180 Days
Online: 365 Days access
Downloadable: 365 Days
Online: 1825 Days access
Downloadable: Lifetime Access

Used Textbook

We're Sorry
Sold Out


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 conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.

Table of Contents

Prefacep. vii
Definition of a Curvep. 1
Vector-valued Functions Depending on Numerical Argumentsp. 5
The Regular Curve and its Representationsp. 9
Straight Line Tangent to a Curvep. 13
Osculating Plane of a Curvep. 17
The Arc Length of a Curvep. 21
The Curvature and Torsion of a Curvep. 27
Osculating Circle of a Plane Curvep. 37
Singular Points of Plane Curvesp. 41
Peano's Curvep. 49
Envelope of the Family of Curvesp. 51
Frenet Formulasp. 53
Determination of a Curve with Given Curvature and Torsionp. 59
Analogies of Curvature and Torsion for Polygonal Linesp. 63
Curves with a Constant Ratio of Curvature and Torsionp. 65
Osculating Spherep. 69
Special Planar Curvesp. 73
Curves in Mechanicsp. 83
Curve Filling a Surfacep. 89
Curves with Locally Convex Projectionp. 91
Integral Inequalities for Closed Curvesp. 97
Reconstruction of a Closed Curve with Given Spherical Indicatrix of Tangentsp. 101
Conditions for a Curve to be Closedp. 103
Isoperimetric Property of a Circlep. 115
One Inequality for a Closed Curvep. 119
Necessary and Sufficient Condition of the Boundedness of a Curve with Periodic Curvature and Torsionp. 121
Delaunay's Problemp. 125
Jordan's Theorem on Closed Plane Curvesp. 133
Gauss's Integral for Two Linked Curvesp. 139
Knotsp. 149
Alexander's Polynomialp. 157
Curves in n-dimensional Euclidean Spacep. 169
Curves with Constant Curvatures in n-dimensional Euclidean Spacep. 177
Generalization of the Fenchel Inequalityp. 183
Knots and Links in Biology and One Mysteryp. 187
Jones' Polynomial, Its Generalization and Some Applicationsp. 191
Referencesp. 199
Indexp. 203
Table of Contents provided by Syndetics. All Rights Reserved.

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.