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Aminov Y. — Differential Geometry and Topology of Curves
Aminov Y. — Differential Geometry and Topology of Curves



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Название: Differential Geometry and Topology of Curves

Автор: Aminov Y.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 205

Добавлена в каталог: 18.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{k}$-regular curve      9
Agnesi's witch      77
Alexander's polynomial      157
Archimedian spiral      75
Astroid      79
Attyah      197
Bakel'man      121
Bar - Natan      197
Barbier's Theorem      35
Bauer      188
Bertrand's curves      176
Bing hypothesis      196
Bitman      196
Cardioid      79
Center of curvature      38
Center of oscillating sphere      70
Cissoid of Diocles      78
Classifying group of knots      154
Closed Jordan curve      3
Conchoids      79
Conway method      195
Crick      187
Curvature angles      63
Curvature of curve      27 171
Curvature of planar curve      31
Curvature with sign      32 57 65
Curve with constant torsion      34
Cusp      4 45 46
Cycloid      79
Definition of elementary curve      2
Definition of envelope      52
Delaunay's problem      125
Diagram of knot      157
DNA      187
Efimov      104
electromagnetic field      86
Elementary curve      2 169
Equation characterizing spherical curves      71
Euclid      1
Evolute      38
Evolvent      38
Fary - Milnor theoiem      99
Fenchel      97 104 183
Feynman diagram      197
Field      197
First approximation      14
First approximationcurvature      170
Fouriei sexes      116
Frank - Kamenezkii      188
Frenet formulas      54 172
Freyd      192
Gauss's integral      140
Gauss's theorem      167
General curve      4
Generator relations of knots      153
Genus of a knot      155
Gorkaviy      183
Gravitation field      85
Group of a knot      150
Hegoi's diagram      196
Helix      66
hilbert      129
Homeomorphism      2
Homfly polynomial      192
Hosle      192
Hurwitz      117
Hypoeydoid      79
Index of a region      158
Intersection index      146
Isolated point      41 45
Isoperimetric property      115
Jones' polynomial      192
Jordan's Theorem      133
Kauffman      197
Klein      1
Knot      149
Knotted curve      99
Lemniscate of Bernoulli      73
Length of a curve      22
Lin      196
Linked curves      139
Listing's, knot      153
Logarithmic spiral      76
Ltckorich      192
Maclaunn's curve      47
Millet      192
Motion      84
Multivectoi      174
Natural paramctnzation      24 170
Nicomede      80
Nikolaevsky      112
normal      16
Ocneanu      192
Osculating plane      17
Osculating point      46
Osculating sphere      69
Oval      35
Parallel force      84
Peano curve      1 49
Phyhppov proof      133
Pohl      188
Polygonal lines      63
Pontryagin      154
Poznjak      101
Principal normal      27
Rectifiable curve      22
Regions of diagram      158
Reidemiestec tiansformations      162
Riemann      2
Roberts      188
Roulets      78
schur      129
Schwartz      129
Second approximation      37
Seifert circle      154
Simple curve      3
Singular point      41
Slope curve      66
Smooth curve      9
Snail of Pascal      81
Spherical mdicatm      97
Steiner      117
Step of helix      67
Support function      117
Tangent      13
Taylor's expansions      7
Throchoids      78
Topological map      2
Torsion angles      63
Torsion of a curve      29
Tractnx      47
Trigonometrical curve      181
Twist      188
Twisting total      144
Vassillev invariants      195
Vector-valued function      5
Veronese      2
Vertices of diagram      158
Vinograd      188
Vygodsky      101
Wallach      196
Watson      187
Weierstrass      125 197
Werner      121
White      144 188
Whitehead's link      194
Whitney number      188
With $n$ foci      75
Witten      196
Writhing number      188
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