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Differential Geometry and Topology of Curves - Yu Animov

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Differential Geometry and Topology of Curves

Name: Differential Geometry and Topology of Curves
Brand: Taylor & Francis Ltd
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By: Yu Animov

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Hardcover | 11 January 2001 | Edition Number 1

At a Glance

Hardcover
216 Pages

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24.77 x 17.15 x 1.91

Hardcover

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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.

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You Can Find This Book In

Non-Fiction Mathematics Geometry Differential & Riemannian Geometry Topology

Preface	p. vii
Definition of a Curve	p. 1
Vector-valued Functions Depending on Numerical Arguments	p. 5
The Regular Curve and its Representations	p. 9
Straight Line Tangent to a Curve	p. 13
Osculating Plane of a Curve	p. 17
The Arc Length of a Curve	p. 21
The Curvature and Torsion of a Curve	p. 27
Osculating Circle of a Plane Curve	p. 37
Singular Points of Plane Curves	p. 41
Peano's Curve	p. 49
Envelope of the Family of Curves	p. 51
Frenet Formulas	p. 53
Determination of a Curve with Given Curvature and Torsion	p. 59
Analogies of Curvature and Torsion for Polygonal Lines	p. 63
Curves with a Constant Ratio of Curvature and Torsion	p. 65
Osculating Sphere	p. 69
Special Planar Curves	p. 73
Curves in Mechanics	p. 83
Curve Filling a Surface	p. 89
Curves with Locally Convex Projection	p. 91
Integral Inequalities for Closed Curves	p. 97
Reconstruction of a Closed Curve with Given Spherical Indicatrix of Tangents	p. 101
Conditions for a Curve to be Closed	p. 103
Isoperimetric Property of a Circle	p. 115
One Inequality for a Closed Curve	p. 119
Necessary and Sufficient Condition of the Boundedness of a Curve with Periodic Curvature and Torsion	p. 121
Delaunay's Problem	p. 125
Jordan's Theorem on Closed Plane Curves	p. 133
Gauss's Integral for Two Linked Curves	p. 139
Knots	p. 149
Alexander's Polynomial	p. 157
Curves in n-dimensional Euclidean Space	p. 169
Curves with Constant Curvatures in n-dimensional Euclidean Space	p. 177
Generalization of the Fenchel Inequality	p. 183
Knots and Links in Biology and One Mystery	p. 187
Jones' Polynomial, Its Generalization and Some Applications	p. 191
References	p. 199
Index	p. 203
Table of Contents provided by Syndetics. All Rights Reserved.

Differential Geometry and Topology of Curves

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